# Load packages
import numpy as np # The 'numpy' package is needed for matrix operations and calculations
import pandas as pd # The 'pandas' package helps us to import and manage data
import math as math # Math package for data cleaning
from scipy import stats # Import scipy.package for confidence intervals
from sklearn.preprocessing import StandardScaler # Import the package for standardizing data
import D47calib as D47c # Import the package for treating clumped isotope data by Daëron and Vermeesch (2023; https://github.com/mdaeron/D47calib)
import matplotlib.pyplot as plt # The 'matplotlib' package contains tools needed to plot our data and results
from matplotlib.patches import Rectangle # The 'Rectangle' function is used to add rectangles to our plots
import seaborn as sns # The 'seaborn' package is used to make our plots look nicer (e.g. enable heatmaps)
import warnings # The 'warnings' package is used to suppress warnings that might occur during the calculations
%matplotlib inline

# Load model SST data as prior and show data structure
IPCC_Atlas_SST = pd.read_csv('Modern case/SSTdat.csv')  # Load the data into Python and in the Jupyter environment.
# Pivot the data to have months as columns and grid cells (lat, lon) as rows
IPCC_Atlas_SST = IPCC_Atlas_SST.pivot(index=['lat', 'lon'], columns='month', values='tos').reset_index()
# Rename months to two-letter codes
month_mapping = {
    'January': 'ja', 'February': 'fb', 'March': 'mr', 'April': 'ar', 'May': 'my', 
    'June': 'jn', 'July': 'jl', 'August': 'ag', 'September': 'sp', 'October': 'ot', 
    'November': 'nv', 'December': 'dc'
}
IPCC_Atlas_SST.rename(columns=month_mapping, inplace=True) # Rename the columns to two-letter codes for months
IPCC_Atlas_SST.head()

# Load model SAT data as prior and show data structure
IPCC_Atlas_SAT = pd.read_csv('Modern case/SATdat.csv')  # Load the data into Python and in the Jupyter environment.
# Pivot the data to have months as columns and grid cells (lat, lon) as rows
IPCC_Atlas_SAT = IPCC_Atlas_SAT.pivot(index=['lat', 'lon'], columns='month', values='tas').reset_index()
# Rename months to two-letter codes
month_mapping = {
    'January': 'ja', 'February': 'fb', 'March': 'mr', 'April': 'ar', 'May': 'my', 
    'June': 'jn', 'July': 'jl', 'August': 'ag', 'September': 'sp', 'October': 'ot', 
    'November': 'nv', 'December': 'dc'
}
IPCC_Atlas_SAT.rename(columns=month_mapping, inplace=True) # Rename the columns to two-letter codes for months
IPCC_Atlas_SAT.head()

# Load HadGEM3 SSS data as prior and show data structure
HadGEM3_SSS = pd.read_csv('Modern case/HadGEM3_SSS_ROI_Panama.csv')  # Load the data into Python and in the Jupyter environment.
# Convert 'timeseries' column to datetime
HadGEM3_SSS['date'] = pd.to_datetime(HadGEM3_SSS['date'], format='%Y-%m-%d')
# Rename longitude and latitude columns to 'lon' and 'lat'
HadGEM3_SSS = HadGEM3_SSS.rename(columns={'longitude': 'lon', 'latitude': 'lat'})

# Extract month as two-letter code
month_abbr = ['ja', 'fb', 'mr', 'ar', 'my', 'jn', 'jl', 'ag', 'sp', 'ot', 'nv', 'dc']
HadGEM3_SSS['month'] = HadGEM3_SSS['date'].dt.month.apply(lambda x: month_abbr[x-1])

# Group by lat, lon, and month, then calculate the mean salinity for each group
HadGEM3_SSS = HadGEM3_SSS.groupby(['lat', 'lon', 'month'], as_index=False)['SSS'].mean()

# Pivot to make one column per month, keeping all data
HadGEM3_SSS = HadGEM3_SSS.pivot(index=['lat', 'lon'], columns='month', values='SSS').reset_index()

# Round latitudes to nearest whole value and subtract 0.5 to align with model grid
HadGEM3_SSS['lat'] = HadGEM3_SSS['lat'].round().astype(int) - 0.5

HadGEM3_SSS.head()

# Load model precip data as prior and show data structure
IPCC_Atlas_precip = pd.read_csv('Modern case/precipdat.csv')  # Load the data into Python and in the Jupyter environment.
# Pivot the data to have months as columns and grid cells (lat, lon) as rows
IPCC_Atlas_precip = IPCC_Atlas_precip.pivot(index=['lat', 'lon'], columns='month', values='pr').reset_index()
# Rename months to two-letter codes
month_mapping = {
    'January': 'ja', 'February': 'fb', 'March': 'mr', 'April': 'ar', 'May': 'my', 
    'June': 'jn', 'July': 'jl', 'August': 'ag', 'September': 'sp', 'October': 'ot', 
    'November': 'nv', 'December': 'dc'
}
IPCC_Atlas_precip.rename(columns=month_mapping, inplace=True) # Rename the columns to two-letter codes for months
IPCC_Atlas_precip.head()

# Merge the datasets of SST, SAT, SSS, and precipitation, force suffixes to be added to the column names
IPCC_Atlas = pd.merge(
    IPCC_Atlas_SST.rename(columns={c: c + '_SST' for c in IPCC_Atlas_SST.columns if c not in ['lat', 'lon']}),
    IPCC_Atlas_SAT.rename(columns={c: c + '_SAT' for c in IPCC_Atlas_SAT.columns if c not in ['lat', 'lon']}),
    on=['lat', 'lon'],
    how='outer'
)

IPCC_Atlas = pd.merge(
    IPCC_Atlas,
    HadGEM3_SSS.rename(columns={c: c + '_SSS' for c in HadGEM3_SSS.columns if c not in ['lat', 'lon']}),
    on=['lat', 'lon'],
    how='outer'
)

IPCC_Atlas = pd.merge(
    IPCC_Atlas,
    IPCC_Atlas_precip.rename(columns={c: c + '_precip' for c in IPCC_Atlas_precip.columns if c not in ['lat', 'lon']}),
    on=['lat', 'lon'],
    how='outer'
)

# Display the combined dataset
IPCC_Atlas.head()

# Create list of month names
months = ['ja', 'fb', 'mr', 'ar', 'my', 'jn', 'jl', 'ag', 'sp', 'ot', 'nv', 'dc']

# Prior SST, SAT, SSS & precipitation estimates from climate models (mean)
mu_prior_SAT_monthly = np.array(IPCC_Atlas[[f"{month}_SAT" for month in months]].mean(axis=0, skipna=True))
mu_prior_SST_monthly = np.array(IPCC_Atlas[[f"{month}_SST" for month in months]].mean(axis=0, skipna=True))
mu_prior_SSS_monthly = np.array(IPCC_Atlas[[f"{month}_SSS" for month in months]].mean(axis=0, skipna=True))
mu_prior_precip_monthly = np.array(IPCC_Atlas[[f"{month}_precip" for month in months]].mean(axis=0, skipna=True))

# Covariance between months in prior SST, SAT, SSS, and precip estimates from climate models (covariance matrix)
cov_prior_SAT_monthly = np.cov(IPCC_Atlas[[f"{month}_SAT" for month in months]].dropna(), rowvar=False)
cov_prior_SST_monthly = np.cov(IPCC_Atlas[[f"{month}_SST" for month in months]].dropna(), rowvar=False)
cov_prior_SSS_monthly = np.cov(IPCC_Atlas[[f"{month}_SSS" for month in months]].dropna(), rowvar=False)
cov_prior_precip_monthly = np.cov(IPCC_Atlas[[f"{month}_precip" for month in months]].dropna(), rowvar=False)

# Store copy of original prior means to keep when later updating the prior
mu_prior_SAT_monthly_original, cov_prior_SAT_monthly_original = mu_prior_SAT_monthly.copy(), cov_prior_SAT_monthly.copy()
mu_prior_SST_monthly_original, cov_prior_SST_monthly_original = mu_prior_SST_monthly.copy(), cov_prior_SST_monthly.copy()
mu_prior_SSS_monthly_original, cov_prior_SSS_monthly_original = mu_prior_SSS_monthly.copy(), cov_prior_SSS_monthly.copy()
mu_prior_precip_monthly_original, cov_prior_precip_monthly_original = mu_prior_precip_monthly.copy(), cov_prior_precip_monthly.copy()

# Extract the standard deviations (uncertainty) from the covariance matrix
std_prior_SAT_monthly = np.sqrt(np.diag(cov_prior_SAT_monthly))
std_prior_SST_monthly = np.sqrt(np.diag(cov_prior_SST_monthly))
std_prior_SSS_monthly = np.sqrt(np.diag(cov_prior_SSS_monthly))
std_prior_precip_monthly = np.sqrt(np.diag(cov_prior_precip_monthly))

print("SAT Monthly Means:", mu_prior_SAT_monthly)
print("SAT Monthly Std Devs:", std_prior_SAT_monthly)
print("SST Monthly Means:", mu_prior_SST_monthly)
print("SST Monthly Std Devs:", std_prior_SST_monthly)
print("SSS Monthly Means:", mu_prior_SSS_monthly)
print("SSS Monthly Std Devs:", std_prior_SSS_monthly)
print("Precip Monthly Means:", mu_prior_precip_monthly)
print("Precip Monthly Std Devs:", std_prior_precip_monthly)

SAT Monthly Means: [26.19674833 26.2856926  26.61780667 26.9355932  26.83360707 26.53449047
 26.469068   26.5685366  26.55148913 26.3253362  26.23056327 26.30819593]
SAT Monthly Std Devs: [0.47312434 0.41409864 0.41961986 0.45581423 0.52380544 0.58817398
 0.60908107 0.63073153 0.65805864 0.67241717 0.66092167 0.57625065]
SST Monthly Means: [27.44732929 26.77931444 26.66707259 27.07042812 27.81826605 28.38219858
 28.62096962 28.7972226  29.09194208 29.15567638 28.99711452 28.42136266]
SST Monthly Std Devs: [0.38677244 0.81134486 1.05313182 1.09679318 1.00268654 0.70288835
 0.47347404 0.48010207 0.46942236 0.53116255 0.47287623 0.36093464]
SSS Monthly Means: [32.9342162  33.62086235 34.05787824 34.33567287 33.89529622 32.50127564
 32.15152274 32.05213394 31.54662009 31.37093452 31.85204499 32.38620964]
SSS Monthly Std Devs: [2.75280482 2.29538948 2.0329931  1.88701351 2.35053874 3.0075095
 2.69062003 2.87471767 3.03645453 2.85139432 2.7804909  2.98121591]
Precip Monthly Means: [ 0.95326442  0.66065841  0.75870658  1.84590803  6.33325375 10.838048
 11.84685843 11.9147063  11.8752223  10.88288037  8.05676985  3.13704099]
Precip Monthly Std Devs: [0.34180364 0.27108401 0.23717466 0.51316878 0.91770655 1.08071996
 1.1180354  1.19916169 1.19446726 1.14380572 0.86132612 0.62397088]

# Set dimensions of data
n_gridcells_monthly = len(IPCC_Atlas["lat"])  # Find the total number of models (use monthly data because monthly data has this column duplicated 3 times)

# Create a monthly scale for the x-axis
month_names = ['January', 'February', 'March', 'April', 'May', 'June', 'July', 'August', 'September', 'October', 'November', 'December']  # List full month names
months_scale = np.arange(len(months)) + 1  # Create monthly scale

# Create the figure and axes
fig, axes = plt.subplots(2, 1, figsize=(10, 12), sharex=True)

# Panel 1: Plot the prior distribution for SST and SAT
axes[0].plot(months_scale, mu_prior_SAT_monthly, label='Prior SAT Mean', marker='o', color='r')
axes[0].plot(months_scale, mu_prior_SST_monthly, label='Prior SST Mean', marker='o', color='b')

# Add 95% confidence intervals for SAT
axes[0].fill_between(
    months_scale,
    mu_prior_SAT_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SAT_monthly / np.sqrt(n_gridcells_monthly),
    mu_prior_SAT_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SAT_monthly / np.sqrt(n_gridcells_monthly),
    alpha=0.2, color='r', label='SAT 95% CI'
)

# Add 95% confidence intervals for SST
axes[0].fill_between(
    months_scale,
    mu_prior_SST_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SST_monthly / np.sqrt(n_gridcells_monthly),
    mu_prior_SST_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SST_monthly / np.sqrt(n_gridcells_monthly),
    alpha=0.2, color='b', label='SST 95% CI'
)

axes[0].set_title('Prior Mean and 95% Confidence Interval for Monthly SST & SAT Values')
axes[0].set_ylabel('Temperature (°C)')
axes[0].legend()
axes[0].grid(True)

# Panel 2: Plot the prior distribution for SSS and precipitation
axes[1].plot(months_scale, mu_prior_SSS_monthly, label='Prior SSS Mean', marker='o', color='g')
ax2 = axes[1].twinx()  # Create a secondary y-axis for precipitation
ax2.plot(months_scale, mu_prior_precip_monthly, label='Prior Precipitation Mean', marker='o', color='purple')

# Add 95% confidence intervals for SSS
axes[1].fill_between(
    months_scale,
    mu_prior_SSS_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SSS_monthly / np.sqrt(n_gridcells_monthly),
    mu_prior_SSS_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SSS_monthly / np.sqrt(n_gridcells_monthly),
    alpha=0.2, color='g', label='SSS 95% CI'
)

# Add 95% confidence intervals for precipitation
ax2.fill_between(
    months_scale,
    mu_prior_precip_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_precip_monthly / np.sqrt(n_gridcells_monthly),
    mu_prior_precip_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_precip_monthly / np.sqrt(n_gridcells_monthly),
    alpha=0.2, color='purple', label='Precipitation 95% CI'
)

axes[1].set_ylabel('SSS (psu)', color='g')
ax2.set_ylabel('Precipitation (mm/day)', color='purple')
axes[1].set_title('Prior Mean and 95% Confidence Interval for Monthly SSS & Precipitation Values')
axes[1].legend(loc='upper left')
ax2.legend(loc='upper right')
axes[1].grid(True)

# Update the x-axis with month names
axes[1].set_xticks(months_scale)
axes[1].set_xticklabels(month_names, rotation=45, ha="right")

[Text(1, 0, 'January'),
 Text(2, 0, 'February'),
 Text(3, 0, 'March'),
 Text(4, 0, 'April'),
 Text(5, 0, 'May'),
 Text(6, 0, 'June'),
 Text(7, 0, 'July'),
 Text(8, 0, 'August'),
 Text(9, 0, 'September'),
 Text(10, 0, 'October'),
 Text(11, 0, 'November'),
 Text(12, 0, 'December')]

# Apply T47()-function from the D47calib package to all SST columns
# Identify the SST and SAT columns separately
SST_columns = [col for col in IPCC_Atlas.columns if col.endswith('_SST')]
SAT_columns = [col for col in IPCC_Atlas.columns if col.endswith('_SAT')]

# Apply the conversion function to the SST and SAT columns and add new columns for D47 and D47_SE
for col in SST_columns:
    base_col_name = col.replace('_SST', '') # Remove the '_SST' suffix from the column name
    IPCC_Atlas[f'{base_col_name}_SST_D47'], IPCC_Atlas[f'{base_col_name}_SST_D47_SE'] = zip(*IPCC_Atlas[col].apply(
        lambda x: D47c.OGLS23.T47(T = x) if not pd.isna(x) else (np.nan, np.nan)
    )) # Use zip() to unpack the tuple returned by the apply() method and apply the T47()-function to each value in the column
for col in SAT_columns:
    base_col_name = col.replace('_SAT', '') # Remove the '_SST' suffix from the column name
    IPCC_Atlas[f'{base_col_name}_SAT_D47'], IPCC_Atlas[f'{base_col_name}_SAT_D47_SE'] = zip(*IPCC_Atlas[col].apply(
        lambda x: D47c.OGLS23.T47(T = x) if not pd.isna(x) else (np.nan, np.nan)
    )) # Use zip() to unpack the tuple returned by the apply() method and apply the T47()-function to each value in the column

# Display the combined data with D47 and D47_SE columns
D47_columns = [col for col in IPCC_Atlas.columns if col.endswith('_D47')]
D47_se_columns = [col for col in IPCC_Atlas.columns if '_D47_SE' in col]
print("D47 values for all grid cells:\n", IPCC_Atlas[D47_columns].head())
print("Calibration standard errors for all grid cells:\n", IPCC_Atlas[D47_se_columns].head())

D47 values for all grid cells:
 month  ar_SST_D47  ag_SST_D47  dc_SST_D47  fb_SST_D47  ja_SST_D47  jl_SST_D47  \
0             NaN         NaN         NaN         NaN         NaN         NaN   
1             NaN         NaN         NaN         NaN         NaN         NaN   
2             NaN         NaN         NaN         NaN         NaN         NaN   
3        0.584869    0.582139    0.583807    0.587368    0.585752    0.582432   
4        0.587996    0.586037    0.583782    0.589082    0.586898    0.585573   

month  jn_SST_D47  mr_SST_D47  my_SST_D47  nv_SST_D47  ...  dc_SAT_D47  \
0             NaN         NaN         NaN         NaN  ...         NaN   
1             NaN         NaN         NaN         NaN  ...         NaN   
2             NaN         NaN         NaN         NaN  ...         NaN   
3        0.582404    0.587211    0.582399    0.583674  ...    0.588737   
4        0.586114    0.589170    0.586742    0.583404  ...    0.588877   

month  fb_SAT_D47  ja_SAT_D47  jl_SAT_D47  jn_SAT_D47  mr_SAT_D47  my_SAT_D47  \
0             NaN         NaN         NaN         NaN         NaN         NaN   
1             NaN         NaN         NaN         NaN         NaN         NaN   
2             NaN         NaN         NaN         NaN         NaN         NaN   
3        0.587915    0.588368    0.589034    0.588636    0.586880    0.586505   
4        0.588662    0.588761    0.589032    0.588700    0.587642    0.587234   

month  nv_SAT_D47  ot_SAT_D47  sp_SAT_D47  
0             NaN         NaN         NaN  
1             NaN         NaN         NaN  
2             NaN         NaN         NaN  
3        0.589746    0.589713    0.588981  
4        0.589790    0.589605    0.588946  

[5 rows x 24 columns]
Calibration standard errors for all grid cells:
 month  ar_SST_D47_SE  ag_SST_D47_SE  dc_SST_D47_SE  fb_SST_D47_SE  \
0                NaN            NaN            NaN            NaN   
1                NaN            NaN            NaN            NaN   
2                NaN            NaN            NaN            NaN   
3           0.001044       0.001042       0.001043       0.001046   
4           0.001047       0.001045       0.001043       0.001048   

month  ja_SST_D47_SE  jl_SST_D47_SE  jn_SST_D47_SE  mr_SST_D47_SE  \
0                NaN            NaN            NaN            NaN   
1                NaN            NaN            NaN            NaN   
2                NaN            NaN            NaN            NaN   
3           0.001045       0.001042       0.001042       0.001046   
4           0.001046       0.001044       0.001045       0.001048   

month  my_SST_D47_SE  nv_SST_D47_SE  ...  dc_SAT_D47_SE  fb_SAT_D47_SE  \
0                NaN            NaN  ...            NaN            NaN   
1                NaN            NaN  ...            NaN            NaN   
2                NaN            NaN  ...            NaN            NaN   
3           0.001042       0.001043  ...       0.001048       0.001047   
4           0.001045       0.001043  ...       0.001048       0.001048   

month  ja_SAT_D47_SE  jl_SAT_D47_SE  jn_SAT_D47_SE  mr_SAT_D47_SE  \
0                NaN            NaN            NaN            NaN   
1                NaN            NaN            NaN            NaN   
2                NaN            NaN            NaN            NaN   
3           0.001047       0.001048       0.001048       0.001046   
4           0.001048       0.001048       0.001048       0.001046   

month  my_SAT_D47_SE  nv_SAT_D47_SE  ot_SAT_D47_SE  sp_SAT_D47_SE  
0                NaN            NaN            NaN            NaN  
1                NaN            NaN            NaN            NaN  
2                NaN            NaN            NaN            NaN  
3           0.001045       0.001049       0.001049       0.001048  
4           0.001046       0.001049       0.001049       0.001048  

[5 rows x 24 columns]

# Apply the d18Ow-SSS function from Graniero et al. (2017) to all SSS columns
# Identify the SSS columns
SSS_columns = [col for col in IPCC_Atlas.columns if col.endswith('_SSS')]

# Apply the conversion function to the SSS columns and add new columns for d18Ow and d18Ow_SE
for col in SSS_columns:
    base_col_name = col.replace('_SSS', '')  # Remove the '_SSS' suffix from the column name
    IPCC_Atlas[f'{base_col_name}_SSS_d18Ow'] = IPCC_Atlas[col].apply(
        lambda x: -7.89 + 0.23 * x if not pd.isna(x) else np.nan  # Calculate d18Ow
    )

# Display the combined data with d18Ow and d18Ow_SE columns
d18Ow_columns = [col for col in IPCC_Atlas.columns if col.endswith('_d18Ow')]
print("d18Ow values for all model outcomes:\n", IPCC_Atlas[d18Ow_columns].head())

d18Ow values for all model outcomes:
 month  ag_SSS_d18Ow  ar_SSS_d18Ow  dc_SSS_d18Ow  fb_SSS_d18Ow  ja_SSS_d18Ow  \
0         -0.946499     -0.535089     -0.651119     -0.776133     -0.910557   
1         -1.054131     -0.510581     -0.922469     -0.802553     -1.029217   
2         -1.122032     -0.454520     -1.155741     -0.802820     -1.078707   
3         -1.054813     -0.320192     -1.168258     -0.733762     -1.099679   
4         -1.385865     -0.244780     -1.411953     -0.468423     -0.918595   

month  jl_SSS_d18Ow  jn_SSS_d18Ow  mr_SSS_d18Ow  my_SSS_d18Ow  nv_SSS_d18Ow  \
0         -0.974017     -0.945143     -0.664774     -0.520886     -0.864359   
1         -0.980658     -1.046126     -0.654697     -0.549428     -0.983300   
2         -1.053387     -1.099166     -0.591658     -0.558844     -1.211089   
3         -1.016603     -1.133604     -0.457816     -0.547296     -1.252933   
4         -1.203919     -1.289815     -0.303092     -0.745229     -1.404130   

month  ot_SSS_d18Ow  sp_SSS_d18Ow  
0         -1.038639     -1.035862  
1         -1.159901     -1.207527  
2         -1.236703     -1.269299  
3         -1.294196     -1.238681  
4         -1.523056     -1.591291

# Iterate over each model and calculate d18Oc values
for index, row in IPCC_Atlas.iterrows():
    # Iterate over each month
    for month in months:
        SST = row[f"{month}_SST"]
        d18Ow = row[f"{month}_SSS_d18Ow"]
        if not pd.isna(SST) and not pd.isna(d18Ow):
            d18Oc = (20.6 - SST) / 4.34 + (d18Ow - 0.27)
        else:
            d18Oc = np.nan
        # Add the calculated d18Oc value to the DataFrame
        IPCC_Atlas.loc[index, f"{month}_d18Oc"] = d18Oc

# Display the updated DataFrame
IPCC_Atlas.head()

# Set the weights of the data based on the standard errors
weights_monthly_SST_D47 = 1 / IPCC_Atlas[[f"{month}_SST_D47_SE" for month in months]] ** 2
weights_monthly_SAT_D47 = 1 / IPCC_Atlas[[f"{month}_SAT_D47_SE" for month in months]] ** 2

# Change the column suffixes from "_D47_SE" to "_D47" in weights_monthly_SST_D47 to match the headers of the D47 matrix later for multiplication
weights_monthly_SST_D47.columns = [col.replace('_SST_D47_SE', '_SST_D47') for col in weights_monthly_SST_D47.columns]
weights_monthly_SAT_D47.columns = [col.replace('_SAT_D47_SE', '_SAT_D47') for col in weights_monthly_SAT_D47.columns]

# Prior D47 estimates from climate models (weighted mean)
mu_prior_SST_D47_monthly = np.array((IPCC_Atlas[[f"{month}_SST_D47" for month in months]] * weights_monthly_SST_D47).sum(axis = 0, skipna = True) / weights_monthly_SST_D47.sum(axis = 0, skipna = True)) # Calculate weighted monthly mean D47 values and convert to numpy array
mu_prior_SAT_D47_monthly = np.array((IPCC_Atlas[[f"{month}_SAT_D47" for month in months]] * weights_monthly_SAT_D47).sum(axis = 0, skipna = True) / weights_monthly_SAT_D47.sum(axis = 0, skipna = True)) # Calculate weighted monthly mean D47 values and convert to numpy array

# Calculate simple (unweighted) mean for monthly d18Ow values
mu_prior_SSS_d18Ow_monthly = np.array(IPCC_Atlas[[f"{month}_SSS_d18Ow" for month in months]].mean(axis=0, skipna=True))
mu_prior_d18Oc_monthly = np.array(IPCC_Atlas[[f"{month}_d18Oc" for month in months]].mean(axis=0, skipna=True))

# Decompose variance within and between model outcomes
model_variances_SST = IPCC_Atlas[[f"{month}_SST_D47" for month in months]].var(axis = 0, ddof = 1)  # Compute variance across models
model_variances_SAT = IPCC_Atlas[[f"{month}_SAT_D47" for month in months]].var(axis = 0, ddof = 1)  # Compute variance across models
model_variances_d18Ow = IPCC_Atlas[[f"{month}_SSS_d18Ow" for month in months]].var(axis = 0, ddof = 1)  # Compute variance across models
model_variances_d18Oc = IPCC_Atlas[[f"{month}_d18Oc" for month in months]].var(axis = 0, ddof = 1)  # Compute variance across models
measurement_variances_SST = (IPCC_Atlas[[f"{month}_SST_D47_SE" for month in months]] ** 2).mean(axis = 0, skipna = True)  # Compute variance on measurements
measurement_variances_SAT = (IPCC_Atlas[[f"{month}_SAT_D47_SE" for month in months]] ** 2).mean(axis = 0, skipna = True)  # Compute variance on measurements

# Covariance between months in prior D47 estimates from climate models (weighted covariance matrix)
cov_raw_monthly_SST = np.cov(IPCC_Atlas[[f"{month}_SST_D47" for month in months]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_raw_monthly_SAT = np.cov(IPCC_Atlas[[f"{month}_SAT_D47" for month in months]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_raw_monthly_d18Ow = np.cov(IPCC_Atlas[[f"{month}_SSS_d18Ow" for month in months]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_raw_monthly_d18Oc = np.cov(IPCC_Atlas[[f"{month}_d18Oc" for month in months]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_prior_SST_D47_monthly = cov_raw_monthly_SST.copy() # Copy covariance matrix to add uncertainty coming from the measurements
cov_prior_SAT_D47_monthly = cov_raw_monthly_SAT.copy() # Copy covariance matrix to add uncertainty coming from the measurements
np.fill_diagonal(cov_prior_SST_D47_monthly, np.diagonal(cov_raw_monthly_SST) + measurement_variances_SST)  # Add diagonal terms for measurement uncertainties (which have no covariance between models)
np.fill_diagonal(cov_prior_SAT_D47_monthly, np.diagonal(cov_raw_monthly_SAT) + measurement_variances_SAT)  # Add diagonal terms for measurement uncertainties (which have no covariance between models)

# Store copy of original prior means to keep when later updating the prior
mu_prior_SST_D47_monthly_original, cov_prior_SST_D47_monthly_original = mu_prior_SST_D47_monthly.copy(), cov_prior_SST_D47_monthly.copy()
mu_prior_SAT_D47_monthly_original, cov_prior_SAT_D47_monthly_original = mu_prior_SAT_D47_monthly.copy(), cov_prior_SAT_D47_monthly.copy()
mu_prior_SSS_d18Ow_monthly_original, cov_prior_SSS_d18Ow_monthly_original = mu_prior_SSS_d18Ow_monthly.copy(), cov_raw_monthly_d18Ow.copy()
mu_prior_d18Oc_monthly_original, cov_prior_d18Oc_monthly_original = mu_prior_d18Oc_monthly.copy(), cov_raw_monthly_d18Oc.copy()

# Extract the standard deviations (uncertainty) from the covariance matrix
std_prior_SST_D47_monthly = np.sqrt(np.diag(cov_prior_SST_D47_monthly))
std_prior_SAT_D47_monthly = np.sqrt(np.diag(cov_prior_SAT_D47_monthly))
std_prior_SSS_d18Ow_monthly = np.sqrt(np.diag(cov_raw_monthly_d18Ow))
std_prior_d18Oc_monthly = np.sqrt(np.diag(cov_raw_monthly_d18Oc))

# Print the results
print("Prior D47 estimates from SST in climate models (weighted mean):")
print(mu_prior_SST_D47_monthly)
print("Prior D47 estimates from SST in climate models (weighted covariance matrix):")
print(std_prior_SST_D47_monthly)
print("Prior D47 estimates from SAT in climate models (weighted mean):")
print(mu_prior_SAT_D47_monthly)
print("Prior D47 estimates from SAT in climate models (weighted covariance matrix):")
print(std_prior_SAT_D47_monthly)
print("Prior d18Ow estimates from SSS in climate models (weighted mean):")
print(mu_prior_SSS_d18Ow_monthly)
print("Prior d18Ow estimates from SSS in climate models (weighted covariance matrix):")
print(std_prior_SSS_d18Ow_monthly)
print("Prior d18Oc estimates from SST and d18Ow in climate models (weighted mean):")
print(mu_prior_d18Oc_monthly)
print("Prior d18Oc estimates from SST and d18Ow in climate models (weighted covariance matrix):")
print(std_prior_d18Oc_monthly)

Prior D47 estimates from SST in climate models (weighted mean):
[0.58611136 0.58807854 0.58840607 0.58721478 0.58502217 0.58337762
 0.5826824  0.58217063 0.58131734 0.58113373 0.58159202 0.58326221]
Prior D47 estimates from SST in climate models (weighted covariance matrix):
[0.00154225 0.00262358 0.0033056  0.00341755 0.00312591 0.00229783
 0.00172489 0.00174205 0.00171518 0.00185845 0.00171988 0.00147969]
Prior D47 estimates from SAT in climate models (weighted mean):
[0.58980992 0.58954575 0.58855954 0.5876189  0.58791991 0.58880551
 0.58899953 0.58870432 0.58875453 0.58942555 0.5897075  0.5894774 ]
Prior D47 estimates from SAT in climate models (weighted covariance matrix):
[0.0017582  0.00161882 0.00162767 0.00170748 0.0018731  0.00203748
 0.00209141 0.00214556 0.00221785 0.00226071 0.00223188 0.00201213]
Prior d18Ow estimates from SSS in climate models (weighted mean):
[-0.31513027 -0.15720166 -0.056688    0.00720476 -0.09408187 -0.4147066
 -0.49514977 -0.51800919 -0.63427738 -0.67468506 -0.56402965 -0.44117178]
Prior d18Ow estimates from SSS in climate models (weighted covariance matrix):
[0.63314511 0.52793958 0.46758841 0.43401311 0.54062391 0.69172719
 0.61884261 0.66118506 0.69838454 0.65582069 0.63951291 0.68567966]
Prior d18Oc estimates from SST and d18Ow in climate models (weighted mean):
[-2.01976487 -1.72743135 -1.62606948 -1.68513392 -2.01588617 -2.38789044
 -2.49384006 -2.58185743 -2.76264532 -2.80414742 -2.66091864 -2.4305927 ]
Prior d18Oc estimates from SST and d18Ow in climate models (weighted covariance matrix):
[0.59701115 0.37039599 0.285586   0.32615673 0.59423465 0.70492047
 0.60946861 0.67389034 0.68550033 0.61192669 0.65277008 0.79771143]

# Plot monthly prior distribution
fig, axes = plt.subplots(2, 2, figsize=(15, 12))  # Adjust the figure to have 2x2 grid

# Plot the prior distribution for SST
axes[0, 0].plot(months_scale, mu_prior_SST_D47_monthly, label='Prior SST Mean', color='b', marker='o')
axes[0, 0].fill_between(months_scale,
                        mu_prior_SST_D47_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SST_D47_monthly / np.sqrt(n_gridcells_monthly),
                        mu_prior_SST_D47_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SST_D47_monthly / np.sqrt(n_gridcells_monthly),
                        color='b', alpha=0.2, label='95% Confidence Interval')
axes[0, 0].set_xticks(months_scale)
axes[0, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 0].set_title('Prior Mean and 95% Confidence Interval for Monthly SST D47 values')
axes[0, 0].set_xlabel('Month')
axes[0, 0].set_ylabel('D47 value')
axes[0, 0].legend()
axes[0, 0].grid(True)

# Plot the prior distribution for SAT
axes[0, 1].plot(months_scale, mu_prior_SAT_D47_monthly, label='Prior SAT Mean', color='r', marker='o')
axes[0, 1].fill_between(months_scale,
                        mu_prior_SAT_D47_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SAT_D47_monthly / np.sqrt(n_gridcells_monthly),
                        mu_prior_SAT_D47_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_SAT_D47_monthly / np.sqrt(n_gridcells_monthly),
                        color='r', alpha=0.2, label='95% Confidence Interval')
axes[0, 1].set_xticks(months_scale)
axes[0, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 1].set_title('Prior Mean and 95% Confidence Interval for Monthly SAT D47 values')
axes[0, 1].set_xlabel('Month')
axes[0, 1].set_ylabel('D47 value')
axes[0, 1].legend()
axes[0, 1].grid(True)

# Plot the prior distribution for d18Oc
axes[1, 0].plot(months_scale, mu_prior_d18Oc_monthly, label='Prior d18Oc Mean', color='purple', marker='o')
axes[1, 0].fill_between(months_scale,
                        mu_prior_d18Oc_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_d18Oc_monthly / np.sqrt(n_gridcells_monthly),
                        mu_prior_d18Oc_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_d18Oc_monthly / np.sqrt(n_gridcells_monthly),
                        color='purple', alpha=0.2, label='95% Confidence Interval')
axes[1, 0].set_xticks(months_scale)
axes[1, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 0].set_title('Prior Mean and 95% Confidence Interval for Monthly d18Oc values')
axes[1, 0].set_xlabel('Month')
axes[1, 0].set_ylabel('d18Oc value')
axes[1, 0].legend()
axes[1, 0].grid(True)

# Plot the prior distribution for precipitation
axes[1, 1].plot(months_scale, mu_prior_precip_monthly, label='Prior Precipitation Mean', color='teal', marker='o')
axes[1, 1].fill_between(months_scale,
                        mu_prior_precip_monthly - stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_precip_monthly / np.sqrt(n_gridcells_monthly),
                        mu_prior_precip_monthly + stats.t.ppf(1 - 0.025, n_gridcells_monthly) * std_prior_precip_monthly / np.sqrt(n_gridcells_monthly),
                        color='teal', alpha=0.2, label='95% Confidence Interval')
axes[1, 1].set_xticks(months_scale)
axes[1, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 1].set_title('Prior Mean and 95% Confidence Interval for Monthly Precipitation values')
axes[1, 1].set_xlabel('Month')
axes[1, 1].set_ylabel('Precipitation (mm/day)')
axes[1, 1].legend()
axes[1, 1].grid(True)

# Update the layout and show the plot
plt.tight_layout()
plt.show()

# Define column names for SAT, SST, d18Oc, and precipitation
SAT_D47_columns_monthly = [f"{month}_SAT_D47" for month in months]
SST_D47_columns_monthly = [f"{month}_SST_D47" for month in months]
d18Oc_columns_monthly = [f"{month}_d18Oc" for month in months]
precip_columns_monthly = [f"{month}_precip" for month in months]

# Extract the relevant columns for SAT, SST D47, d18Oc, and precipitation
SAT_D47_columns_monthly = [f"{month}_SAT_D47" for month in months]
SST_D47_columns_monthly = [f"{month}_SST_D47" for month in months]
d18Oc_columns_monthly = [f"{month}_d18Oc" for month in months]
precip_columns_monthly = [f"{month}_precip" for month in months]

# Combine the relevant columns into a single dataframe
combined_data_monthly = IPCC_Atlas[SAT_D47_columns_monthly + SST_D47_columns_monthly + d18Oc_columns_monthly + precip_columns_monthly]

# Calculate the covariance matrix for the combined data
cov_combined_monthly = np.cov(combined_data_monthly.dropna(), rowvar=False)

# Plot the heatmap of the raw combined covariance matrix
plt.figure(figsize=(12, 10))
sns.heatmap(
    cov_combined_monthly,  # Use the raw covariance matrix
    annot=False,
    fmt=".2f",
    cmap="coolwarm",
    center=0,
    xticklabels=SAT_D47_columns_monthly + SST_D47_columns_monthly + d18Oc_columns_monthly + precip_columns_monthly,
    yticklabels=SAT_D47_columns_monthly + SST_D47_columns_monthly + d18Oc_columns_monthly + precip_columns_monthly
)

# Add titles to the axes per parameter
plt.axvline(x=len(SAT_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly), color='black', linestyle='--', linewidth=1)

plt.axhline(y=len(SAT_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly), color='black', linestyle='--', linewidth=1)

# Add parameter labels
plt.text(len(SAT_D47_columns_monthly) / 2, -2, 'D47 value from SAT', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) / 2, -2, 'D47 value from SST', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) / 2, -2, 'd18Oc', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) + len(precip_columns_monthly) / 2, -2, 'Precipitation', ha='center', va='center', fontsize=10)

plt.text(-2, len(SAT_D47_columns_monthly) / 2, 'D47 value from SAT', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-2, len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) / 2, 'D47 value from SST', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-2, len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) / 2, 'd18Oc', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-2, len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) + len(precip_columns_monthly) / 2, 'Precipitation', ha='center', va='center', rotation=90, fontsize=10)

plt.title("Raw Combined Covariance Matrix")
plt.show()

# Normalize each submatrix independently for better visualization
def normalize_matrix(matrix):
    min_val = np.min(matrix)
    max_val = np.max(matrix)
    return (matrix - min_val) / (max_val - min_val)

# Extract the relevant columns for SAT, SST D47, d18Oc, and precipitation
SAT_D47_columns_monthly = [f"{month}_SAT_D47" for month in months]
SST_D47_columns_monthly = [f"{month}_SST_D47" for month in months]
d18Oc_columns_monthly = [f"{month}_d18Oc" for month in months]
precip_columns_monthly = [f"{month}_precip" for month in months]

# Combine the relevant columns into a single dataframe
combined_data_monthly = IPCC_Atlas[SAT_D47_columns_monthly + SST_D47_columns_monthly + d18Oc_columns_monthly + precip_columns_monthly]

# Calculate the covariance matrix for the combined data
cov_combined_monthly = np.cov(combined_data_monthly.dropna(), rowvar=False)

# Extract the covariance matrices for SAT D47, SST D47, d18Oc, and precipitation
cov_SAT_D47_monthly = cov_combined_monthly[:len(months), :len(months)]
cov_SST_D47_monthly = cov_combined_monthly[len(months):2*len(months), len(months):2*len(months)]
cov_d18Oc_monthly = cov_combined_monthly[2*len(months):3*len(months), 2*len(months):3*len(months)]
cov_precip_monthly = cov_combined_monthly[3*len(months):, 3*len(months):]

# Extract the cross-covariance matrices
cross_cov_SAT_SST_D47_monthly = cov_combined_monthly[:len(months), len(months):2*len(months)]
cross_cov_SAT_d18Oc_monthly = cov_combined_monthly[:len(months), 2*len(months):3*len(months)]
cross_cov_SAT_precip_monthly = cov_combined_monthly[:len(months), 3*len(months):]
cross_cov_SST_d18Oc_monthly = cov_combined_monthly[len(months):2*len(months), 2*len(months):3*len(months)]
cross_cov_SST_precip_monthly = cov_combined_monthly[len(months):2*len(months), 3*len(months):]
cross_cov_d18Oc_precip_monthly = cov_combined_monthly[2*len(months):3*len(months), 3*len(months):]

# Normalize each submatrix
normalized_cov_SAT_D47_monthly = normalize_matrix(cov_SAT_D47_monthly)
normalized_cov_SST_D47_monthly = normalize_matrix(cov_SST_D47_monthly)
normalized_cov_d18Oc_monthly = normalize_matrix(cov_d18Oc_monthly)
normalized_cov_precip_monthly = normalize_matrix(cov_precip_monthly)

# Normalize each cross-covariance matrix
normalized_cross_cov_SAT_SST_D47_monthly = normalize_matrix(cross_cov_SAT_SST_D47_monthly)
normalized_cross_cov_SAT_d18Oc_monthly = normalize_matrix(cross_cov_SAT_d18Oc_monthly)
normalized_cross_cov_SAT_precip_monthly = normalize_matrix(cross_cov_SAT_precip_monthly)
normalized_cross_cov_SST_d18Oc_monthly = normalize_matrix(cross_cov_SST_d18Oc_monthly)
normalized_cross_cov_SST_precip_monthly = normalize_matrix(cross_cov_SST_precip_monthly)
normalized_cross_cov_d18Oc_precip_monthly = normalize_matrix(cross_cov_d18Oc_precip_monthly)

# Combine the normalized submatrices into a single normalized covariance matrix
normalized_cov_combined_monthly = np.block([
    [normalized_cov_SAT_D47_monthly, normalized_cross_cov_SAT_SST_D47_monthly, normalized_cross_cov_SAT_d18Oc_monthly, normalized_cross_cov_SAT_precip_monthly],
    [normalized_cross_cov_SAT_SST_D47_monthly.T, normalized_cov_SST_D47_monthly, normalized_cross_cov_SST_d18Oc_monthly, normalized_cross_cov_SST_precip_monthly],
    [normalized_cross_cov_SAT_d18Oc_monthly.T, normalized_cross_cov_SST_d18Oc_monthly.T, normalized_cov_d18Oc_monthly, normalized_cross_cov_d18Oc_precip_monthly],
    [normalized_cross_cov_SAT_precip_monthly.T, normalized_cross_cov_SST_precip_monthly.T, normalized_cross_cov_d18Oc_precip_monthly.T, normalized_cov_precip_monthly]
])

# Plot the heatmap of the normalized combined covariance matrix
plt.figure(figsize=(12, 10))
sns.heatmap(
    normalized_cov_combined_monthly,
    annot=False,
    fmt=".2f",
    cmap="coolwarm",
    center=0,
    xticklabels=SAT_D47_columns_monthly + SST_D47_columns_monthly + d18Oc_columns_monthly + precip_columns_monthly,
    yticklabels=SAT_D47_columns_monthly + SST_D47_columns_monthly + d18Oc_columns_monthly + precip_columns_monthly
)

# Add titles to the axes per parameter
plt.axvline(x=len(SAT_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly), color='black', linestyle='--', linewidth=1)

plt.axhline(y=len(SAT_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly), color='black', linestyle='--', linewidth=1)

# Add parameter labels
plt.text(len(SAT_D47_columns_monthly) / 2, -2, 'D47 value from SAT', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) / 2, -2, 'D47 value from SST', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) / 2, -2, 'd18Oc', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) + len(precip_columns_monthly) / 2, -2, 'Precipitation', ha='center', va='center', fontsize=10)

plt.text(-7, len(SAT_D47_columns_monthly) / 2, 'D47 value from SAT', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-7, len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) / 2, 'D47 value from SST', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-7, len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) / 2, 'd18Oc', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-7, len(SAT_D47_columns_monthly) + len(SST_D47_columns_monthly) + len(d18Oc_columns_monthly) + len(precip_columns_monthly) / 2, 'Precipitation', ha='center', va='center', rotation=90, fontsize=10)

plt.title("Normalized Combined Covariance Matrix")
plt.show()

# Combine the prior means of D47 and SAT into a single state vector
mu_prior_monthly_combined = np.concatenate((mu_prior_SST_D47_monthly, mu_prior_SAT_D47_monthly, mu_prior_d18Oc_monthly, mu_prior_precip_monthly))

# Combine the covariance matrices of D47 values of SST and SAT, including the cross-covariance
cov_prior_monthly_combined = cov_combined_monthly.copy()

# Define the seasons
seasons = {
    "winter": ["dc", "ja", "fb"],
    "spring": ["mr", "ar", "my"],
    "summer": ["jn", "jl", "ag"],
    "autumn": ["sp", "ot", "nv"],
}

# Stack monthly columns to create seasonal dataframes
# Initialize dictionaries to store seasonal data
IPCC_Atlas_seasonal_dict = {}

# Identify the columns to process (all except the modelname column)
columns_to_process = [col for col in IPCC_Atlas.columns if any(suffix in col for suffix in [
    '_SST', '_SAT', '_SST_D47', '_SST_D47_SE', '_SAT_D47', '_SAT_D47_SE',
    '_SSS', '_d18Oc', '_precip'
])]

# Process each season
for season, months in seasons.items():  # Iterate over the seasons and corresponding months
    for col in columns_to_process:  # Iterate over the columns to process
        base_col_name = col.split('_')[0]  # Extract the base column name
        suffix = '_'.join(col.split('_')[1:])  # Extract the suffix
        if base_col_name in months:  # Check if the column corresponds to the current season
            season_col_name = f"{season}_{suffix}"  # Create the new column name
            if season_col_name not in IPCC_Atlas_seasonal_dict:  # Check if the new column name already exists in the seasonal data
                IPCC_Atlas_seasonal_dict[season_col_name] = []  # If not, initialize a new column in the seasonal data means
            IPCC_Atlas_seasonal_dict[season_col_name].append(IPCC_Atlas[col])

# Combine the seasonal data into a single dataframe
IPCC_Atlas_seasonal = pd.DataFrame()
for season_col_name, data in IPCC_Atlas_seasonal_dict.items():
    # Concatenate the data for each season and reshape it properly
    concatenated_data = pd.concat(data, axis=0).reset_index(drop=True)
    IPCC_Atlas_seasonal[season_col_name] = concatenated_data

# Add model names
IPCC_Atlas_seasonal["lat"] = np.tile(IPCC_Atlas["lat"].values, 3)  # Repeat the model names for each season
IPCC_Atlas_seasonal["lon"] = np.tile(IPCC_Atlas["lon"].values, 3)  # Repeat the model names for each season

# Display the new seasonal DataFrame
D47_columns_seasonal = [col for col in IPCC_Atlas_seasonal.columns if col.endswith('_D47')]
D47_se_columns_seasonal = [col for col in IPCC_Atlas_seasonal.columns if '_D47_SE' in col]
SSS_columns_seasonal = [col for col in IPCC_Atlas_seasonal.columns if col.endswith('_SSS')]
d18Oc_columns_seasonal = [col for col in IPCC_Atlas_seasonal.columns if col.endswith('_d18Oc')]
precip_columns_seasonal = [col for col in IPCC_Atlas_seasonal.columns if col.endswith('_precip')]

print("Seasonal D47 values for all SST model outcomes:\n", IPCC_Atlas_seasonal[D47_columns_seasonal].head())
print("Calibration standard errors for all SST model outcomes:\n", IPCC_Atlas_seasonal[D47_se_columns_seasonal].head())
print("Seasonal SSS values for all model outcomes:\n", IPCC_Atlas_seasonal[SSS_columns_seasonal].head())
print("Seasonal d18Oc values for all model outcomes:\n", IPCC_Atlas_seasonal[d18Oc_columns_seasonal].head())
print("Seasonal precipitation values for all model outcomes:\n", IPCC_Atlas_seasonal[precip_columns_seasonal].head())

Seasonal D47 values for all SST model outcomes:
    winter_SST_D47  winter_SAT_D47  spring_SST_D47  spring_SAT_D47  \
0             NaN             NaN             NaN             NaN   
1             NaN             NaN             NaN             NaN   
2             NaN             NaN             NaN             NaN   
3        0.583807        0.588737        0.584869        0.585712   
4        0.583782        0.588877        0.587996        0.586618   

   summer_SST_D47  summer_SAT_D47  autumn_SST_D47  autumn_SAT_D47  
0             NaN             NaN             NaN             NaN  
1             NaN             NaN             NaN             NaN  
2             NaN             NaN             NaN             NaN  
3        0.582139        0.588755        0.583674        0.589746  
4        0.586037        0.588803        0.583404        0.589790  
Calibration standard errors for all SST model outcomes:
    winter_SST_D47_SE  winter_SAT_D47_SE  spring_SST_D47_SE  spring_SAT_D47_SE  \
0                NaN                NaN                NaN                NaN   
1                NaN                NaN                NaN                NaN   
2                NaN                NaN                NaN                NaN   
3           0.001043           0.001048           0.001044           0.001044   
4           0.001043           0.001048           0.001047           0.001045   

   summer_SST_D47_SE  summer_SAT_D47_SE  autumn_SST_D47_SE  autumn_SAT_D47_SE  
0                NaN                NaN                NaN                NaN  
1                NaN                NaN                NaN                NaN  
2                NaN                NaN                NaN                NaN  
3           0.001042           0.001048           0.001043           0.001049  
4           0.001045           0.001048           0.001043           0.001049  
Seasonal SSS values for all model outcomes:
    winter_SSS  spring_SSS  summer_SSS  autumn_SSS
0   31.473394   31.977873   30.189136   30.546265
1   30.293614   32.084429   29.721171   30.029132
2   29.279388   32.328173   29.425948   29.038743
3   29.224964   32.912211   29.718203   28.856813
4   28.165424   33.240089   28.278848   28.199434
Seasonal d18Oc values for all model outcomes:
    winter_d18Oc  spring_d18Oc  summer_d18Oc  autumn_d18Oc
0           NaN           NaN           NaN           NaN
1           NaN           NaN           NaN           NaN
2           NaN           NaN           NaN           NaN
3     -2.975600     -2.219563     -3.273769     -3.374633
4     -2.704737     -1.912361     -3.137344     -3.505681
Seasonal precipitation values for all model outcomes:
    winter_precip  spring_precip  summer_precip  autumn_precip
0            NaN            NaN            NaN            NaN
1            NaN            NaN            NaN            NaN
2            NaN            NaN            NaN            NaN
3       2.590541       1.689385      12.423080       7.746123
4       2.881293       1.779216      12.493553       7.909942

# Prior estimates from climate models (mean)
mu_prior_SAT_seasonal = np.array(IPCC_Atlas_seasonal[[f"{season}_SAT" for season in seasons]].mean(axis=0, skipna=True))
mu_prior_SST_seasonal = np.array(IPCC_Atlas_seasonal[[f"{season}_SST" for season in seasons]].mean(axis=0, skipna=True))
mu_prior_SSS_seasonal = np.array(IPCC_Atlas_seasonal[[f"{season}_SSS" for season in seasons]].mean(axis=0, skipna=True))
mu_prior_precip_seasonal = np.array(IPCC_Atlas_seasonal[[f"{season}_precip" for season in seasons]].mean(axis=0, skipna=True))

# Covariance between seasons in prior estimates from climate models (covariance matrix)
cov_prior_SAT_seasonal = np.cov(IPCC_Atlas_seasonal[[f"{season}_SAT" for season in seasons]].dropna(), rowvar=False)
cov_prior_SST_seasonal = np.cov(IPCC_Atlas_seasonal[[f"{season}_SST" for season in seasons]].dropna(), rowvar=False)
cov_prior_SSS_seasonal = np.cov(IPCC_Atlas_seasonal[[f"{season}_SSS" for season in seasons]].dropna(), rowvar=False)
cov_prior_precip_seasonal = np.cov(IPCC_Atlas_seasonal[[f"{season}_precip" for season in seasons]].dropna(), rowvar=False)

# Store copy of original prior means to keep when later updating the prior
mu_prior_SAT_seasonal_original, cov_prior_SAT_seasonal_original = mu_prior_SAT_seasonal.copy(), cov_prior_SAT_seasonal.copy()
mu_prior_SST_seasonal_original, cov_prior_SST_seasonal_original = mu_prior_SST_seasonal.copy(), cov_prior_SST_seasonal.copy()
mu_prior_SSS_seasonal_original, cov_prior_SSS_seasonal_original = mu_prior_SSS_seasonal.copy(), cov_prior_SSS_seasonal.copy()
mu_prior_precip_seasonal_original, cov_prior_precip_seasonal_original = mu_prior_precip_seasonal.copy(), cov_prior_precip_seasonal.copy()

# Extract the standard deviations (uncertainty) from the covariance matrix
std_prior_SAT_seasonal = np.sqrt(np.diag(cov_prior_SAT_seasonal))
std_prior_SST_seasonal = np.sqrt(np.diag(cov_prior_SST_seasonal))
std_prior_SSS_seasonal = np.sqrt(np.diag(cov_prior_SSS_seasonal))
std_prior_precip_seasonal = np.sqrt(np.diag(cov_prior_precip_seasonal))

# Print the results
print("SAT Seasonal Means:", mu_prior_SAT_seasonal)
print("SAT Seasonal Std Devs:", std_prior_SAT_seasonal)
print("SST Seasonal Means:", mu_prior_SST_seasonal)
print("SST Seasonal Std Devs:", std_prior_SST_seasonal)
print("SSS Seasonal Means:", mu_prior_SSS_seasonal)
print("SSS Seasonal Std Devs:", std_prior_SSS_seasonal)
print("Precipitation Seasonal Means:", mu_prior_precip_seasonal)
print("Precipitation Seasonal Std Devs:", std_prior_precip_seasonal)

SAT Seasonal Means: [26.26354562 26.79566898 26.52403169 26.36912953]
SAT Seasonal Std Devs: [0.48353899 0.47684737 0.59702245 0.66270196]
SST Seasonal Means: [27.54933547 27.18525559 28.60013027 29.08157766]
SST Seasonal Std Devs: [0.87357802 1.13352575 0.5748445  0.48432974]
SSS Seasonal Means: [32.9804294  34.09628244 32.23497744 31.58986653]
SSS Seasonal Std Devs: [2.69635668 2.07310351 2.82074275 2.85149091]
Precipitation Seasonal Means: [ 1.5836546   2.97928946 11.53320424 10.27162417]
Precipitation Seasonal Std Devs: [1.19706106 2.51465787 1.21440914 1.94491224]

# Define the seasons, number of models, and scale for the x-axis
seasons = ["winter", "spring", "summer", "autumn"]
n_gridcells_seasonal = len(IPCC_Atlas["lat"])  # Find the total number of models
seasons_scale = np.arange(len(seasons)) + 1  # Create seasonal scale

# Create a 1x2 plotting grid
fig, axes = plt.subplots(2, 1, figsize=(10, 10))

# Panel 1: Plot the prior distribution for SST and SAT
axes[0].plot(seasons_scale, mu_prior_SST_seasonal, label='Prior SST Mean', marker='o', color='b')
axes[0].fill_between(
    seasons_scale,
    mu_prior_SST_seasonal - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SST_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_SST_seasonal + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SST_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='b', label='SST 95% CI'
)
axes[0].plot(seasons_scale, mu_prior_SAT_seasonal, label='Prior SAT Mean', marker='o', color='r')
axes[0].fill_between(
    seasons_scale,
    mu_prior_SAT_seasonal - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SAT_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_SAT_seasonal + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SAT_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='r', label='SAT 95% CI'
)
axes[0].set_title('Prior Mean and 95% Confidence Interval for Seasonal SST & SAT')
axes[0].set_xlabel('Season')
axes[0].set_ylabel('Temperature (°C)')
axes[0].set_xticks(seasons_scale)
axes[0].set_xticklabels(seasons)
axes[0].legend()
axes[0].grid(True)

# Panel 2: Plot the prior distribution for SSS and precipitation
axes[1].plot(seasons_scale, mu_prior_SSS_seasonal, label='Prior SSS Mean', marker='o', color='g')
ax2 = axes[1].twinx()  # Create a secondary y-axis for precipitation
ax2.plot(seasons_scale, mu_prior_precip_seasonal, label='Prior Precipitation Mean', marker='o', color='purple')

# Add 95% confidence intervals for SSS
axes[1].fill_between(
    seasons_scale,
    mu_prior_SSS_seasonal - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SSS_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_SSS_seasonal + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SSS_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='g', label='SSS 95% CI'
)

# Add 95% confidence intervals for precipitation
ax2.fill_between(
    seasons_scale,
    mu_prior_precip_seasonal - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_precip_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_precip_seasonal + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_precip_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='purple', label='Precipitation 95% CI'
)

axes[1].set_title('Prior Mean and 95% Confidence Interval for Seasonal SSS & Precipitation')
axes[1].set_xlabel('Season')
axes[1].set_ylabel('SSS (psu)', color='g')
ax2.set_ylabel('Precipitation (mm/day)', color='purple')
axes[1].set_xticks(seasons_scale)
axes[1].set_xticklabels(seasons)
axes[1].legend(loc='upper left')
ax2.legend(loc='upper right')
axes[1].grid(True)

# Adjust layout and show the plot
plt.tight_layout()
plt.show()

# Set the weights of the data based on the standard errors
weights_seasonal_SST_D47 = 1 / IPCC_Atlas_seasonal[[f"{season}_SST_D47_SE" for season in seasons]] ** 2
weights_seasonal_SAT_D47 = 1 / IPCC_Atlas_seasonal[[f"{season}_SAT_D47_SE" for season in seasons]] ** 2

# Change the column suffixes from "_D47_SE" to "_D47" in weights_seasonal to match the headers of the D47 matrix later for multiplication
weights_seasonal_SST_D47.columns = [col.replace('_SST_D47_SE', '_SST_D47') for col in weights_seasonal_SST_D47.columns]
weights_seasonal_SAT_D47.columns = [col.replace('_SAT_D47_SE', '_SAT_D47') for col in weights_seasonal_SAT_D47.columns]

# Prior D47 estimates from climate models (weighted mean)
mu_prior_SST_D47_seasonal = np.array((IPCC_Atlas_seasonal[[f"{season}_SST_D47" for season in seasons]] * weights_seasonal_SST_D47).sum(axis = 0, skipna = True) / weights_seasonal_SST_D47.sum(axis = 0, skipna = True)) # Calculate weighted seasonal mean D47 values and convert to numpy array
mu_prior_SAT_D47_seasonal = np.array((IPCC_Atlas_seasonal[[f"{season}_SAT_D47" for season in seasons]] * weights_seasonal_SAT_D47).sum(axis = 0, skipna = True) / weights_seasonal_SAT_D47.sum(axis = 0, skipna = True)) # Calculate weighted seasonal mean D47 values and convert to numpy array

# Calculate simple (unweighted) mean for monthly d18Oc values
mu_prior_d18Oc_seasonal = np.array(IPCC_Atlas_seasonal[[f"{season}_d18Oc" for season in seasons]].mean(axis=0, skipna=True))
mu_prior_precip_seasonal = np.array(IPCC_Atlas_seasonal[[f"{season}_precip" for season in seasons]].mean(axis=0, skipna=True))

# Decompose variance within and between model outcomes
model_variances_SST_D47 = IPCC_Atlas_seasonal[[f"{season}_SST_D47" for season in seasons]].var(axis = 0, ddof = 1)  # Compute variance across models
model_variances_SAT_D47 = IPCC_Atlas_seasonal[[f"{season}_SAT_D47" for season in seasons]].var(axis = 0, ddof = 1)  # Compute variance across models
measurement_variances_SST_D47 = (IPCC_Atlas_seasonal[[f"{season}_SST_D47_SE" for season in seasons]] ** 2).mean(axis = 0, skipna = True)  # Compute variance on measurements
measurement_variances_SAT_D47 = (IPCC_Atlas_seasonal[[f"{season}_SAT_D47_SE" for season in seasons]] ** 2).mean(axis = 0, skipna = True)  # Compute variance on measurements

# Covariance between seasons in prior D47 estimates from climate models (weighted covariance matrix)
cov_raw_seasonal_SST_D47 = np.cov(IPCC_Atlas_seasonal[[f"{season}_SST_D47" for season in seasons]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_raw_seasonal_SAT_D47 = np.cov(IPCC_Atlas_seasonal[[f"{season}_SAT_D47" for season in seasons]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_raw_seasonal_d18Oc = np.cov(IPCC_Atlas_seasonal[[f"{season}_d18Oc" for season in seasons]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_raw_seasonal_precip = np.cov(IPCC_Atlas_seasonal[[f"{season}_precip" for season in seasons]].dropna(), rowvar = False)  # Compute the covariance matrix for the raw data (without measurement uncertainty)
cov_prior_SST_D47_seasonal = cov_raw_seasonal_SST_D47.copy()  # Copy covariance matrix to add uncertainty coming from the measurements
cov_prior_SAT_D47_seasonal = cov_raw_seasonal_SAT_D47.copy()  # Copy covariance matrix to add uncertainty coming from the measurements
cov_prior_d18Oc_seasonal = cov_raw_seasonal_d18Oc.copy()  # Copy covariance matrix to add uncertainty coming from the measurements
cov_prior_precip_seasonal = cov_raw_seasonal_precip.copy()  # Copy covariance matrix to add uncertainty coming from the measurements
np.fill_diagonal(cov_prior_SST_D47_seasonal, np.diagonal(cov_raw_seasonal_SST_D47) + measurement_variances_SST_D47)  # Add diagonal terms for measurement uncertainties (which have no covariance between models)
np.fill_diagonal(cov_prior_SAT_D47_seasonal, np.diagonal(cov_raw_seasonal_SAT_D47) + measurement_variances_SAT_D47)  # Add diagonal terms for measurement uncertainties (which have no covariance between models)

# Store copy of original prior means to keep when later updating the prior
mu_prior_SST_D47_seasonal_original, cov_prior_SST_D47_seasonal_original = mu_prior_SST_D47_seasonal.copy(), cov_prior_SST_D47_seasonal.copy()
mu_prior_SAT_D47_seasonal_original, cov_prior_SAT_D47_seasonal_original = mu_prior_SAT_D47_seasonal.copy(), cov_prior_SAT_D47_seasonal.copy()
mu_prior_d18Oc_seasonal_original, cov_prior_d18Oc_seasonal_original = mu_prior_d18Oc_seasonal.copy(), cov_raw_seasonal_d18Oc.copy()
mu_prior_precip_seasonal_original, cov_prior_precip_seasonal_original = mu_prior_precip_seasonal.copy(), cov_raw_seasonal_precip.copy()

# Extract the standard deviations (uncertainty) from the covariance matrix
std_prior_SST_D47_seasonal = np.sqrt(np.diag(cov_prior_SST_D47_seasonal))
std_prior_SAT_D47_seasonal = np.sqrt(np.diag(cov_prior_SAT_D47_seasonal))
std_prior_d18Oc_seasonal = np.sqrt(np.diag(cov_prior_d18Oc_seasonal))
std_prior_precip_seasonal = np.sqrt(np.diag(cov_prior_precip_seasonal))

print("mu_prior_SST_D47_seasonal:", mu_prior_SST_D47_seasonal)
print("std_prior_SST_D47_seasonal:", std_prior_SST_D47_seasonal)
print("mu_prior_SAT_D47_seasonal:", mu_prior_SAT_D47_seasonal)
print("std_prior_SAT_D47_seasonal:", std_prior_SAT_D47_seasonal)
print("mu_prior_d18Oc_seasonal:", mu_prior_d18Oc_seasonal)
print("std_prior_d18Oc_seasonal:", std_prior_d18Oc_seasonal)
print("mu_prior_precip_seasonal:", mu_prior_precip_seasonal)
print("std_prior_precip_seasonal:", std_prior_precip_seasonal)

mu_prior_SST_D47_seasonal: [0.58581025 0.58687706 0.58274323 0.58134767]
std_prior_SST_D47_seasonal: [0.00277616 0.00351338 0.00197095 0.00174785]
mu_prior_SAT_D47_seasonal: [0.58961097 0.58803244 0.58883642 0.58929545]
std_prior_SAT_D47_seasonal: [0.00178228 0.00175895 0.00205975 0.00223382]
mu_prior_d18Oc_seasonal: [-2.05926297 -1.77569652 -2.48786265 -2.74257046]
std_prior_d18Oc_seasonal: [0.66384694 0.44756316 0.64969896 0.63483524]
mu_prior_precip_seasonal: [ 1.5836546   2.97928946 11.53320424 10.27162417]
std_prior_precip_seasonal: [1.19706106 2.51465787 1.21440914 1.94491224]

# Define the seasons, number of models, and scale for the x-axis
seasons = ["winter", "spring", "summer", "autumn"]
n_gridcells_seasonal = len(IPCC_Atlas["lat"])  # Find the total number of models (use monthly data because seasonal data has this column duplicated 3 times)
seasons_scale = np.arange(len(seasons)) + 1  # Create seasonal scale

# Create a 2x2 plotting grid
fig, axes = plt.subplots(2, 2, figsize=(15, 12))

# Panel 1: Plot the prior distribution for SST D47 values
axes[0, 0].plot(seasons_scale, mu_prior_SST_D47_seasonal[:len(seasons)], label='Prior SST D47 Mean', marker='o', color='b')
axes[0, 0].fill_between(
    seasons_scale,
    mu_prior_SST_D47_seasonal[:len(seasons)] - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SST_D47_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_SST_D47_seasonal[:len(seasons)] + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SST_D47_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='b', label='95% Confidence Interval'
)
axes[0, 0].set_title('Prior Mean and 95% Confidence Interval for Seasonal SST D47 Values')
axes[0, 0].set_xlabel('Season')
axes[0, 0].set_ylabel('D47 Value')
axes[0, 0].set_xticks(seasons_scale)
axes[0, 0].set_xticklabels(seasons)
axes[0, 0].legend()
axes[0, 0].grid(True)

# Panel 2: Plot the prior distribution for SAT D47 values
axes[0, 1].plot(seasons_scale, mu_prior_SAT_D47_seasonal[:len(seasons)], label='Prior SAT D47 Mean', marker='o', color='r')
axes[0, 1].fill_between(
    seasons_scale,
    mu_prior_SAT_D47_seasonal[:len(seasons)] - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SAT_D47_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_SAT_D47_seasonal[:len(seasons)] + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_SAT_D47_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='r', label='95% Confidence Interval'
)
axes[0, 1].set_title('Prior Mean and 95% Confidence Interval for Seasonal SAT D47 Values')
axes[0, 1].set_xlabel('Season')
axes[0, 1].set_ylabel('D47 Value')
axes[0, 1].set_xticks(seasons_scale)
axes[0, 1].set_xticklabels(seasons)
axes[0, 1].legend()
axes[0, 1].grid(True)

# Panel 3: Plot the prior distribution for d18Oc
axes[1, 0].plot(seasons_scale, mu_prior_d18Oc_seasonal, label='Prior d18Oc Mean', marker='o', color='g')
axes[1, 0].fill_between(
    seasons_scale,
    mu_prior_d18Oc_seasonal - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_d18Oc_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_d18Oc_seasonal + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_d18Oc_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='g', label='95% Confidence Interval'
)
axes[1, 0].set_title('Prior Mean and 95% Confidence Interval for Seasonal d18Oc Values')
axes[1, 0].set_xlabel('Season')
axes[1, 0].set_ylabel('d18Oc Value')
axes[1, 0].set_xticks(seasons_scale)
axes[1, 0].set_xticklabels(seasons)
axes[1, 0].legend()
axes[1, 0].grid(True)

# Panel 4: Plot the prior distribution for precipitation
axes[1, 1].plot(seasons_scale, mu_prior_precip_seasonal, label='Prior Precipitation Mean', marker='o', color='purple')
axes[1, 1].fill_between(
    seasons_scale,
    mu_prior_precip_seasonal - stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_precip_seasonal / np.sqrt(n_gridcells_seasonal),
    mu_prior_precip_seasonal + stats.t.ppf(1 - 0.025, n_gridcells_seasonal) * std_prior_precip_seasonal / np.sqrt(n_gridcells_seasonal),
    alpha=0.2, color='purple', label='95% Confidence Interval'
)
axes[1, 1].set_title('Prior Mean and 95% Confidence Interval for Seasonal Precipitation Values')
axes[1, 1].set_xlabel('Season')
axes[1, 1].set_ylabel('Precipitation (mm/day)')
axes[1, 1].set_xticks(seasons_scale)
axes[1, 1].set_xticklabels(seasons)
axes[1, 1].legend()
axes[1, 1].grid(True)

# Adjust layout and show the plot
plt.tight_layout()
plt.show()

# Extract the relevant columns for SST, SAT D47, d18Oc, and precipitation
SST_D47_columns_seasonal = [f"{season}_SST_D47" for season in seasons]
SAT_D47_columns_seasonal = [f"{season}_SAT_D47" for season in seasons]
d18Oc_columns_seasonal = [f"{season}_d18Oc" for season in seasons]
precip_columns_seasonal = [f"{season}_precip" for season in seasons]

# Combine the relevant columns into a single dataframe
combined_data_seasonal = IPCC_Atlas_seasonal[
    SST_D47_columns_seasonal + SAT_D47_columns_seasonal + d18Oc_columns_seasonal + precip_columns_seasonal
]

# Calculate the covariance matrix for the combined data
cov_combined_seasonal = np.cov(combined_data_seasonal.dropna(), rowvar=False)

# Extract the covariance matrices for each variable
cov_SST_D47_seasonal = cov_combined_seasonal[:len(seasons), :len(seasons)]
cov_SAT_D47_seasonal = cov_combined_seasonal[len(seasons):2*len(seasons), len(seasons):2*len(seasons)]
cov_d18Oc_seasonal = cov_combined_seasonal[2*len(seasons):3*len(seasons), 2*len(seasons):3*len(seasons)]
cov_precip_seasonal = cov_combined_seasonal[3*len(seasons):, 3*len(seasons):]

# Extract the cross-covariance matrices
cross_cov_SST_SAT_D47_seasonal = cov_combined_seasonal[:len(seasons), len(seasons):2*len(seasons)]
cross_cov_SST_d18Oc_seasonal = cov_combined_seasonal[:len(seasons), 2*len(seasons):3*len(seasons)]
cross_cov_SST_precip_seasonal = cov_combined_seasonal[:len(seasons), 3*len(seasons):]
cross_cov_SAT_d18Oc_seasonal = cov_combined_seasonal[len(seasons):2*len(seasons), 2*len(seasons):3*len(seasons)]
cross_cov_SAT_precip_seasonal = cov_combined_seasonal[len(seasons):2*len(seasons), 3*len(seasons):]
cross_cov_d18Oc_precip_seasonal = cov_combined_seasonal[2*len(seasons):3*len(seasons), 3*len(seasons):]

# Plot a heatmap of the combined covariance matrix
plt.figure(figsize=(12, 10))
sns.heatmap(
    np.round(cov_combined_seasonal * 10**4, 1),  # Scale by 10^4 for better visualization and round values
    annot=False,
    fmt=".2f",
    cmap="coolwarm",
    center=0,
    xticklabels=SST_D47_columns_seasonal + SAT_D47_columns_seasonal + d18Oc_columns_seasonal + precip_columns_seasonal,
    yticklabels=SST_D47_columns_seasonal + SAT_D47_columns_seasonal + d18Oc_columns_seasonal + precip_columns_seasonal
)

# Add titles to the axes per parameter
plt.axvline(x=len(SST_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal) + len(d18Oc_columns_seasonal), color='black', linestyle='--', linewidth=1)

plt.axhline(y=len(SST_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal) + len(d18Oc_columns_seasonal), color='black', linestyle='--', linewidth=1)

# Add parameter labels
plt.text(len(SST_D47_columns_seasonal) / 2, -2, 'SST D47', ha='center', va='center', fontsize=10)
plt.text(len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal) / 2, -2, 'SAT D47', ha='center', va='center', fontsize=10)
plt.text(len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal) + len(d18Oc_columns_seasonal) / 2, -2, 'd18Oc', ha='center', va='center', fontsize=10)
plt.text(len(SST_D47_columns_seasonal) + len(SAT_D47_columns_seasonal) + len(d18Oc_columns_seasonal) + len(precip_columns_seasonal) / 2, -2, 'Precipitation', ha='center', va='center', fontsize=10)

plt.title("Combined Covariance Matrix for SST D47, SAT D47, d18Oc, and Precipitation")
plt.show()

# Normalize each submatrix independently for better visualization
def normalize_matrix(matrix):
    min_val = np.min(matrix)
    max_val = np.max(matrix)
    return (matrix - min_val) / (max_val - min_val)

# Extract the covariance matrices for SAT D47, SST D47, d18Oc, and precipitation
cov_SAT_D47_seasonal = cov_combined_seasonal[:len(seasons), :len(seasons)]
cov_SST_D47_seasonal = cov_combined_seasonal[len(seasons):2*len(seasons), len(seasons):2*len(seasons)]
cov_d18Oc_seasonal = cov_combined_seasonal[2*len(seasons):3*len(seasons), 2*len(seasons):3*len(seasons)]
cov_precip_seasonal = cov_combined_seasonal[3*len(seasons):, 3*len(seasons):]

# Extract the cross-covariance matrices
cross_cov_SAT_SST_D47_seasonal = cov_combined_seasonal[:len(seasons), len(seasons):2*len(seasons)]
cross_cov_SAT_d18Oc_seasonal = cov_combined_seasonal[:len(seasons), 2*len(seasons):3*len(seasons)]
cross_cov_SAT_precip_seasonal = cov_combined_seasonal[:len(seasons), 3*len(seasons):]
cross_cov_SST_d18Oc_seasonal = cov_combined_seasonal[len(seasons):2*len(seasons), 2*len(seasons):3*len(seasons)]
cross_cov_SST_precip_seasonal = cov_combined_seasonal[len(seasons):2*len(seasons), 3*len(seasons):]
cross_cov_d18Oc_precip_seasonal = cov_combined_seasonal[2*len(seasons):3*len(seasons), 3*len(seasons):]

# Normalize each submatrix
normalized_cov_SAT_D47_seasonal = normalize_matrix(cov_SAT_D47_seasonal)
normalized_cov_SST_D47_seasonal = normalize_matrix(cov_SST_D47_seasonal)
normalized_cov_d18Oc_seasonal = normalize_matrix(cov_d18Oc_seasonal)
normalized_cov_precip_seasonal = normalize_matrix(cov_precip_seasonal)

# Normalize each cross-covariance matrix
normalized_cross_cov_SAT_SST_D47_seasonal = normalize_matrix(cross_cov_SAT_SST_D47_seasonal)
normalized_cross_cov_SAT_d18Oc_seasonal = normalize_matrix(cross_cov_SAT_d18Oc_seasonal)
normalized_cross_cov_SAT_precip_seasonal = normalize_matrix(cross_cov_SAT_precip_seasonal)
normalized_cross_cov_SST_d18Oc_seasonal = normalize_matrix(cross_cov_SST_d18Oc_seasonal)
normalized_cross_cov_SST_precip_seasonal = normalize_matrix(cross_cov_SST_precip_seasonal)
normalized_cross_cov_d18Oc_precip_seasonal = normalize_matrix(cross_cov_d18Oc_precip_seasonal)

# Combine the normalized submatrices into a single normalized covariance matrix
normalized_cov_combined_seasonal = np.block([
    [normalized_cov_SAT_D47_seasonal, normalized_cross_cov_SAT_SST_D47_seasonal, normalized_cross_cov_SAT_d18Oc_seasonal, normalized_cross_cov_SAT_precip_seasonal],
    [normalized_cross_cov_SAT_SST_D47_seasonal.T, normalized_cov_SST_D47_seasonal, normalized_cross_cov_SST_d18Oc_seasonal, normalized_cross_cov_SST_precip_seasonal],
    [normalized_cross_cov_SAT_d18Oc_seasonal.T, normalized_cross_cov_SST_d18Oc_seasonal.T, normalized_cov_d18Oc_seasonal, normalized_cross_cov_d18Oc_precip_seasonal],
    [normalized_cross_cov_SAT_precip_seasonal.T, normalized_cross_cov_SST_precip_seasonal.T, normalized_cross_cov_d18Oc_precip_seasonal.T, normalized_cov_precip_seasonal]
])

# Plot the heatmap of the normalized combined covariance matrix
plt.figure(figsize=(12, 10))
sns.heatmap(
    normalized_cov_combined_seasonal,
    annot=False,
    fmt=".2f",
    cmap="coolwarm",
    center=0,
    xticklabels=SAT_D47_columns_seasonal + SST_D47_columns_seasonal + d18Oc_columns_seasonal + precip_columns_seasonal,
    yticklabels=SAT_D47_columns_seasonal + SST_D47_columns_seasonal + d18Oc_columns_seasonal + precip_columns_seasonal
)

# Add titles to the axes per parameter
plt.axvline(x=len(SAT_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axvline(x=len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) + len(d18Oc_columns_seasonal), color='black', linestyle='--', linewidth=1)

plt.axhline(y=len(SAT_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal), color='black', linestyle='--', linewidth=1)
plt.axhline(y=len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) + len(d18Oc_columns_seasonal), color='black', linestyle='--', linewidth=1)

# Add parameter labels
plt.text(len(SAT_D47_columns_seasonal) / 2, -1, 'D47 value from SAT', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) / 2, -1, 'D47 value from SST', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) + len(d18Oc_columns_seasonal) / 2, -1, 'd18Oc', ha='center', va='center', fontsize=10)
plt.text(len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) + len(d18Oc_columns_seasonal) + len(precip_columns_seasonal) / 2, -1, 'Precipitation', ha='center', va='center', fontsize=10)

plt.text(-3, len(SAT_D47_columns_seasonal) / 2, 'D47 value from SAT', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-3, len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) / 2, 'D47 value from SST', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-3, len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) + len(d18Oc_columns_seasonal) / 2, 'd18Oc', ha='center', va='center', rotation=90, fontsize=10)
plt.text(-3, len(SAT_D47_columns_seasonal) + len(SST_D47_columns_seasonal) + len(d18Oc_columns_seasonal) + len(precip_columns_seasonal) / 2, 'Precipitation', ha='center', va='center', rotation=90, fontsize=10)

plt.title("Normalized Combined Covariance Matrix")
plt.show()

# Combine the prior means of D47 and SAT into a single state vector
mu_prior_seasonal_combined = np.concatenate((mu_prior_SST_D47_seasonal, mu_prior_SAT_D47_seasonal, mu_prior_d18Oc_seasonal, mu_prior_precip_seasonal))

# Combine the covariance matrices of D47 values of SST and SAT, d18Oc and precipitation including the cross-covariance
cov_prior_seasonal_combined = cov_combined_seasonal.copy()

# Load measurements and format them into a dictionary
# These are the actual individual D47 measurements and ShellChron outcomes and thus come with a time uncertainty which can be propagated.
Caldarescu_data = pd.read_csv('Modern case/Caldarescu_data.csv') # Load the data into Python and in the Jupyter environment.
Caldarescu_data_dict = Caldarescu_data.to_dict('records') # Convert to dictionary with column headers as keys

# Convert estimated day of year to month (0-11) and season (0-3), set errors to 0
for record in Caldarescu_data_dict:
    doy = record.get("Estimated day of year", np.nan)
    if not pd.isna(doy):
        record["month_score"] = int(doy / 365 * 12) % 12  # month index 0-11
        record["season_score"] = int(doy / 365 * 4) % 4    # season index 0-3
    else:
        record["month_score"] = np.nan
        record["season_score"] = np.nan
    record["Month_err"] = 0
    record["Season_err"] = 0

# Print excerpt of the dictionary to check format
print(Caldarescu_data_dict[1])

{'SampName': 'M5_115', 'Specimen': 'M5', 'SampNum': 115, 'Time of year': 'Apr/Oct', 'Increment number': 2, 'Estimated date': '01/10/2005', 'Estimated day of year': 273.0, 'Final_d13Ccarb': -0.01, 'd13C_SD': 0.030214895, 'Final_d18Ocarb_VPDB': -4.32, 'd18O_SD': 0.059240652, 'D47rfac': 0.644, 'D47': 0.582, 'D47_SD': 0.039056165, 'month_score': 8, 'season_score': 2, 'Month_err': 0, 'Season_err': 0}

# Extract measurements and uncertainties from the dictionary, skipping missing values
D47_measurements_individual = [measurement["D47"] for measurement in Caldarescu_data_dict if not pd.isna(measurement["D47"])] # Extract the D47 values
d18Oc_measurements_individual = [measurement["Final_d18Ocarb_VPDB"] for measurement in Caldarescu_data_dict if not pd.isna(measurement["Final_d18Ocarb_VPDB"])] # Extract the d18Oc values
D47_measurement_uncertainties_individual = [measurement["D47_SD"] ** 2 for measurement in Caldarescu_data_dict if not pd.isna(measurement["D47"])] # Square the standard deviation to get the variance
d18Oc_measurement_uncertainties_individual = [measurement["d18O_SD"] ** 2 for measurement in Caldarescu_data_dict if not pd.isna(measurement["Final_d18Ocarb_VPDB"])] # Square the standard deviation to get the variance

# Create the measurement matrix Z
Z_individual = np.array(D47_measurements_individual + d18Oc_measurements_individual).reshape(-1, 1)

# Create the measurement uncertainty matrix R (diagonal matrix)
R_individual = np.diag(D47_measurement_uncertainties_individual + d18Oc_measurement_uncertainties_individual) # Diagonal matrix of measurement uncertainties

# Create the observation matrix H for monthly data based on individual measurements
N_measurements = len(Z_individual)
H_monthly = np.zeros((N_measurements, len(mu_prior_monthly_combined)))

# Fill the first part of the observation matrix H with ones at the positions corresponding to the D47 measurements, ignoring NaN values
for i, measurement in enumerate([m for m in Caldarescu_data_dict if not pd.isna(m["D47"])]):
    time_index = int(measurement["month_score"])
    H_monthly[i, time_index] = 1  # Indexing the first set of columns (1:12) for SST_D47

# Fill the second part of the observation matrix H with ones at the positions corresponding to the d18Oc measurements, ignoring NaN values
for i, measurement in enumerate([m for m in Caldarescu_data_dict if not pd.isna(m["Final_d18Ocarb_VPDB"])]):
    time_index = int(measurement["month_score"])
    H_monthly[i + len(D47_measurements_individual), time_index + 24] = 1  # Indexing the third column block (25:36) for d18Oc

print(H_monthly)

[[0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]
 ...
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]]

# Create the observation matrix H for seasonal data based on individual measurements

# Number of seasonally averaged measurements
H_seasonal = np.zeros((N_measurements, len(mu_prior_seasonal_combined)))

# Fill the first part of the observation matrix H with ones at the positions corresponding to the D47 measurements, ignoring NaN values
for i, measurement in enumerate([m for m in Caldarescu_data_dict if not pd.isna(m["D47"])]):
    time_index = int(measurement["season_score"])
    H_seasonal[i, time_index] = 1  # Indexing the first set of columns (1:4) for SST_D47

# Fill the second part of the observation matrix H with ones at the positions corresponding to the d18Oc measurements, ignoring NaN values
for i, measurement in enumerate([m for m in Caldarescu_data_dict if not pd.isna(m["Final_d18Ocarb_VPDB"])]):
    time_index = int(measurement["season_score"])
    H_seasonal[i + len(D47_measurements_individual), time_index + 8] = 1  # Indexing the third column block (8:12) for d18Oc

print(H_seasonal)

[[0. 0. 1. ... 0. 0. 0.]
 [0. 0. 1. ... 0. 0. 0.]
 [0. 0. 1. ... 0. 0. 0.]
 ...
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]]

# Define the list of season names for integer indexing
season_names = ["winter", "spring", "summer", "autumn"]

# Initialize dictionaries to store aggregated measurements and uncertainties per season
D47_measurements_seasonal = {season: [] for season in season_names}
d18Oc_measurements_seasonal = {season: [] for season in season_names}
D47_measurement_uncertainties_seasonal = {season: [] for season in season_names}
d18Oc_measurement_uncertainties_seasonal = {season: [] for season in season_names}
print(D47_measurements_seasonal)

for measurement in Caldarescu_data_dict:
    if not pd.isna(measurement["D47"]):
        season_index = int(measurement["season_score"])
        D47_measurements_seasonal[season_names[season_index]].append(measurement["D47"])
        D47_measurement_uncertainties_seasonal[season_names[season_index]].append(measurement["D47_SD"] ** 2)
    if not pd.isna(measurement["Final_d18Ocarb_VPDB"]):
        season_index = int(measurement["season_score"])
        d18Oc_measurements_seasonal[season_names[season_index]].append(measurement["Final_d18Ocarb_VPDB"])
        d18Oc_measurement_uncertainties_seasonal[season_names[season_index]].append(measurement["d18O_SD"] ** 2)

# Calculate weighted mean and propagated uncertainty for each season
D47_aggregated_measurements_seasonal = []
d18Oc_aggregated_measurements_seasonal = []
D47_aggregated_uncertainties_seasonal = []
d18Oc_aggregated_uncertainties_seasonal = []

for season in season_names:
    if D47_measurements_seasonal[season]:
        weights = 1 / np.array(D47_measurement_uncertainties_seasonal[season])
        weighted_mean = np.sum(np.array(D47_measurements_seasonal[season]) * weights) / np.sum(weights)
        measurement_variance = np.var(D47_measurements_seasonal[season], ddof=1)
        propagated_uncertainty = np.sqrt(1 / np.sum(weights) + measurement_variance)
        propagated_standard_error = propagated_uncertainty / np.sqrt(len(D47_measurements_seasonal[season])) # Assemble D47 data as SE (optional)
        D47_aggregated_measurements_seasonal.append(weighted_mean)
        D47_aggregated_uncertainties_seasonal.append(propagated_uncertainty ** 2)
    if d18Oc_measurements_seasonal[season]:
        weights = 1 / np.array(d18Oc_measurement_uncertainties_seasonal[season])
        weighted_mean = np.sum(np.array(d18Oc_measurements_seasonal[season]) * weights) / np.sum(weights)
        measurement_variance = np.var(d18Oc_measurements_seasonal[season], ddof=1)
        propagated_uncertainty = np.sqrt(1 / np.sum(weights) + measurement_variance)
        d18Oc_aggregated_measurements_seasonal.append(weighted_mean)
        d18Oc_aggregated_uncertainties_seasonal.append(propagated_uncertainty ** 2)

# OPTIONAL: Lower boundary d18Oc varaince at 0.01 (equivalent to 0.1 per mil measuremetn uncertainty)
d18Oc_aggregated_uncertainties_seasonal = [max(uncertainty, 0.01) for uncertainty in d18Oc_aggregated_uncertainties_seasonal]

# Create the measurement matrix Z
Z_seasonal_aggregated = np.array(D47_aggregated_measurements_seasonal + d18Oc_aggregated_measurements_seasonal).reshape(-1, 1)

# Create the measurement uncertainty matrix R (diagonal matrix)
R_seasonal_aggregated = np.diag(D47_aggregated_uncertainties_seasonal + d18Oc_aggregated_uncertainties_seasonal)  # Diagonal matrix of measurement uncertainties

print("Z_seasonal_aggregated:", Z_seasonal_aggregated)
print("R_seasonal_aggregated:", R_seasonal_aggregated)

{'winter': [], 'spring': [], 'summer': [], 'autumn': []}
Z_seasonal_aggregated: [[ 0.6203526 ]
 [ 0.60752459]
 [ 0.58873077]
 [ 0.60630233]
 [-1.66855491]
 [-2.19754098]
 [-4.05653846]
 [-2.77790698]]
R_seasonal_aggregated: [[2.25072127e-03 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 2.33469318e-03 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 7.07753232e-04 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 1.88021380e-03
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  1.22199900e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 1.46025638e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 1.43614517e-01 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 7.42231892e-01]]

# Create the observation matrix H for seasonally aggregated data

# Define the number of seasons or months
num_seasons = 4

# Number of seasonally aggregated measurements
N_measurements_seasonal_aggregated = len(Z_seasonal_aggregated)
H_seasonal_aggregated = np.zeros((N_measurements_seasonal_aggregated, len(mu_prior_seasonal_combined)))

# Fill the observation matrix H with ones at the positions corresponding to the measurements
for i, measurement in enumerate(Z_seasonal_aggregated):
    if i < N_measurements_seasonal_aggregated // 2:
        time_index = i % num_seasons  # Ensure the index is within the range of seasons
        H_seasonal_aggregated[i, time_index] = 1
    else:
        time_index = i % num_seasons
        H_seasonal_aggregated[i, time_index + 8] = 1

print(H_seasonal_aggregated)

[[1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]]

month_names = ['January', 'February', 'March', 'April', 'May', 'June', 'July', 'August', 'September', 'October', 'November', 'December']  # List full month names

# Initialize dictionaries to store aggregated measurements and uncertainties per month
D47_measurements_monthly = {month: [] for month in month_names}
d18Oc_measurements_monthly = {month: [] for month in month_names}
D47_measurement_uncertainties_monthly = {month: [] for month in month_names}
d18Oc_measurement_uncertainties_monthly = {month: [] for month in month_names}

# Aggregate measurements and uncertainties per month
for measurement in Caldarescu_data_dict:
    if not pd.isna(measurement["D47"]):
        month_index = int(measurement["month_score"])
        D47_measurements_monthly[month_names[month_index]].append(measurement["D47"])
        D47_measurement_uncertainties_monthly[month_names[month_index]].append(measurement["D47_SD"] ** 2)
    if not pd.isna(measurement["Final_d18Ocarb_VPDB"]):
        month_index = int(measurement["month_score"])
        d18Oc_measurements_monthly[month_names[month_index]].append(measurement["Final_d18Ocarb_VPDB"])
        d18Oc_measurement_uncertainties_monthly[month_names[month_index]].append(measurement["d18O_SD"] ** 2)

# Calculate weighted mean and propagated uncertainty for each month
D47_aggregated_measurements_monthly = []
d18Oc_aggregated_measurements_monthly = []
D47_aggregated_uncertainties_monthly = []
d18Oc_aggregated_uncertainties_monthly = []

for month in month_names:
    if D47_measurements_monthly[month]:
        weights = 1 / np.array(D47_measurement_uncertainties_monthly[month])
        weighted_mean = np.sum(np.array(D47_measurements_monthly[month]) * weights) / np.sum(weights)
        measurement_variance = np.var(D47_measurements_monthly[month], ddof=1)
        propagated_uncertainty = np.sqrt(1 / np.sum(weights) + measurement_variance)
        propagated_standard_error = propagated_uncertainty / np.sqrt(len(D47_measurements_monthly[month]))  # Assemble D47 data as SE (optional)
        D47_aggregated_measurements_monthly.append(weighted_mean)
        D47_aggregated_uncertainties_monthly.append(propagated_uncertainty ** 2) # Assemble D47 data as SE
    if d18Oc_measurements_monthly[month]:
        weights = 1 / np.array(d18Oc_measurement_uncertainties_monthly[month])
        weighted_mean = np.sum(np.array(d18Oc_measurements_monthly[month]) * weights) / np.sum(weights)
        measurement_variance = np.var(d18Oc_measurements_monthly[month], ddof=1)
        propagated_uncertainty = np.sqrt(1 / np.sum(weights) + measurement_variance)
        d18Oc_aggregated_measurements_monthly.append(weighted_mean)
        d18Oc_aggregated_uncertainties_monthly.append(propagated_uncertainty ** 2)

# OPTIONAL: Lower boundary d18Oc varaince at 0.01 (equivalent to 0.1 per mil measurement uncertainty)
d18Oc_aggregated_uncertainties_monthly = [max(uncertainty, 0.01) for uncertainty in d18Oc_aggregated_uncertainties_monthly]

# Create the measurement matrix Z
Z_monthly_aggregated = np.array(D47_aggregated_measurements_monthly + d18Oc_aggregated_measurements_monthly).reshape(-1, 1)

# Create the measurement uncertainty matrix R (diagonal matrix)
R_monthly_aggregated = np.diag(D47_aggregated_uncertainties_monthly + d18Oc_aggregated_uncertainties_monthly)  # Diagonal matrix of measurement uncertainties

print("Z_monthly_aggregated:", Z_monthly_aggregated)
print("R_monthly_aggregated:", R_monthly_aggregated)

Z_monthly_aggregated: [[ 0.60602128]
 [ 0.62462903]
 [ 0.62673437]
 [ 0.60375   ]
 [ 0.61565217]
 [ 0.5994    ]
 [ 0.594375  ]
 [ 0.58444444]
 [ 0.588     ]
 [ 0.61542857]
 [ 0.616375  ]
 [ 0.60114286]
 [-2.8387234 ]
 [-1.22677419]
 [-1.2371875 ]
 [-1.7525    ]
 [-2.16      ]
 [-3.53      ]
 [-3.66625   ]
 [-4.02333333]
 [-4.43666667]
 [-1.96142857]
 [-1.995     ]
 [-3.20571429]]
R_monthly_aggregated: [[2.09378060e-03 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 2.79716801e-03 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 1.74234975e-03 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 2.70733911e-03
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  2.41664911e-03 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 1.56013840e-03 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 8.77226574e-04 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 1.29751489e-03
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  4.15987114e-04 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 8.05531051e-04 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 1.12751229e-03 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 2.47134573e-03
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  3.77755613e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 8.29783733e-01 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 8.54456323e-01 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 1.26294478e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  1.37155258e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 1.00000000e-02 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 1.53511819e-02 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 2.60399394e-02
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  9.39399394e-02 0.00000000e+00 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 1.00000000e-02 0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 3.35243961e-02 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00 0.00000000e+00 6.01039623e-01]]

# Create the observation matrix H for monthly aggregated data

# Define the number of seasons or months
num_months = 12

# Number of monthly aggregated measurements
N_measurements_monthly_aggregated = len(Z_monthly_aggregated)
H_monthly_aggregated = np.zeros((N_measurements_monthly_aggregated, len(mu_prior_monthly_combined)))

# Fill the observation matrix H with ones at the positions corresponding to the measurements
for i, measurement in enumerate(Z_monthly_aggregated):
    if i < N_measurements_monthly_aggregated // 2:
        time_index = i % num_months  # Ensure the index is within the range of months
        H_monthly_aggregated[i, time_index] = 1
    else:
        time_index = i % num_months
        H_monthly_aggregated[i, time_index + 24] = 1

print(H_monthly_aggregated)

[[1. 0. 0. ... 0. 0. 0.]
 [0. 1. 0. ... 0. 0. 0.]
 [0. 0. 1. ... 0. 0. 0.]
 ...
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]
 [0. 0. 0. ... 0. 0. 0.]]

def kalman_update_block(
    mu_prior: np.ndarray,
    cov_prior: np.ndarray,
    Z: np.ndarray,
    R: np.ndarray,
    H: np.ndarray,
    debug_print: bool = False
):
    """
    Perform a Kalman update step for a block of observations.

    Parameters:
    mu_prior (np.ndarray): The prior mean vector.
    cov_prior (np.ndarray): The prior covariance matrix.
    Z (np.ndarray): The measurement matrix.
    R (np.ndarray): The measurement noise covariance matrix.
    H (np.ndarray): The observation matrix.
    debug_print (bool): If True, print debug statements.

    Returns:
    mu_posterior (np.ndarray): The posterior mean vector.
    cov_posterior (np.ndarray): The posterior covariance matrix.
    """
    if debug_print:
        # Print shapes of key variables for debugging
        print("Shape of cov_prior:", cov_prior.shape)
        print("Shape of H:", H.shape)
        print("Shape of R:", R.shape)
        print("Shape of mu_prior:", mu_prior.shape)
        print("Shape of Z:", Z.shape)

    # Compute the Kalman gain
    K = cov_prior @ H.T @ np.linalg.inv(H @ cov_prior @ H.T + R)
    if debug_print:
        print("Shape of K:", K.shape)

    # In-between steps for debugging
    Y_hat = H @ mu_prior  # Compute the predicted observation
    if debug_print:
        print("Shape of Y_hat:", Y_hat.shape)
    innovation = Z - Y_hat.reshape(-1, 1)  # Compute the innovation
    if debug_print:
        print("Shape of innovation:", innovation.shape)
    kalman_gain = K @ innovation  # Compute the Kalman gain
    if debug_print:
        print("Shape of kalman_gain:", kalman_gain.shape)

    # Update the posterior mean estimate
    mu_posterior = mu_prior + kalman_gain.flatten()

    # Update the posterior covariance estimate
    cov_posterior = cov_prior - K @ H @ cov_prior

    return mu_posterior, cov_posterior

# Create function to keep track of the likelihood statistics and data

# Suppress FutureWarning
# warnings.simplefilter(action = 'ignore', category = FutureWarning)

def likelihood_statistics_multi(
    weighted_sum,
    effective_weights_total,
    n_update,
    data_library,
    measurement,
    timestamp,
    timestamp_sd,
    Variable_names = ["Variable_name1", "Variable_name2"],
    Variable_names_SDs = ["Variable_name_SD1", "Variable_name_SD2"]
):
    """
    Incrementally updates the likelihood statistics for seasonal data.

    Parameters:
    - weighted_sum: list
        List tracking the mean times the effective weight for each time bin and variable.
    - effective_weights_total: list
        List tracking the sum of effective weights for each time bin and variable.
    - n_update: list
        List tracking the number of datapoints for each time bin and variable.
    - data_library: dict
        Dictionary tracking individual data points and their uncertainties.
    - measurement: dict
        A single measurement containing data on multiple variables.
    - timestamp: str
        Key in the measurement dictionary for the timestamp (0-based index).
    - timestamp_sd: float
        Standard deviation of uncertainty in the timestamp.
    - Variable_name: list of str
        Key in the measurement dictionary for the variables (e.g. d18Oc, D47).
    - Variable_name_SD: list of str
        Key in the measurement dictionary for the standard deviation on the variables (e.g. d18Oc, D47).
    """
    # Check if at least one combination of variable name and its SD is present in the measurement
    found = False
    for var_name, var_sd_name in zip(Variable_names, Variable_names_SDs):
        if var_name in measurement and var_sd_name in measurement:
            found = True
            break

    if timestamp in measurement and found:
        # Extract the time and data values from the measurement
        time = measurement[timestamp]
        time_sd = measurement[timestamp_sd]
        # Loop through all variable/SD pairs
        for var_name, var_sd_name in zip(Variable_names, Variable_names_SDs):
            if var_name in measurement and var_sd_name in measurement:
                data_val = measurement[var_name]
                data_sd = measurement[var_sd_name]
                
                # Check if the data is valid
                if not np.isnan(data_val) and not np.isnan(data_sd):
                    # Calculate the weight (inverse of variance)
                    weight = 1 / (data_sd ** 2)

                    # Determine the number of bins
                    num_bins_seasonal = int(len(weighted_sum) / len(Variable_names))
                    # Ensure num_bins_seasonal is an integer
                    bin_indices = np.arange(num_bins_seasonal, dtype=np.float64)

                    # Calculate the probability density for each bin
                    if time_sd == 0:  # Catch cases where the time uncertainty is zero (or unknown)
                        probabilities = np.zeros(num_bins_seasonal, dtype=np.float64)
                        bin_index = int(time) % num_bins_seasonal  # Ensure the bin index is within range
                        probabilities[bin_index] = 1  # Set the probability to 1 for the correct bin
                    else:
                        probabilities = stats.norm.pdf(bin_indices, loc=time, scale=time_sd)  # For non-zero time uncertainty, use a normal distribution
                        probabilities /= probabilities.sum()  # Normalize to ensure the sum of probabilities is 1

                    for i, prob in enumerate(probabilities):  # Loop over all possible bin numbers in the probability vector
                        bin_index = i % num_bins_seasonal  # Wrap around to the first bin if it overflows

                        # Update the weighted sums and sample count
                        effective_weight = weight * prob
                        var_idx = Variable_names.index(var_name)  # Find the index of the variable
                        idx = int(var_idx * num_bins_seasonal + bin_index)  # Unique index for (variable, bin)
                        if weighted_sum[idx] is None:
                            weighted_sum[idx] = 0
                            effective_weights_total[idx] = 0
                        weighted_sum[idx] = weighted_sum[idx] + data_val * effective_weight
                        effective_weights_total[idx] = effective_weights_total[idx] + effective_weight

                    # Update n_update for the correct variable and bin
                    var_idx = Variable_names.index(var_name) # Find the index of the variable
                    n_update[var_idx * num_bins_seasonal + (int(time) % num_bins_seasonal)] += 1  # update sample number per bin and variable

                    # Track individual data points and their uncertainties
                    key = (var_name, int(time)) # Store individual data points in a dictionary with (variable, time) as key
                    if key not in data_library:
                        data_library[key] = []  # Initialize the list for a new (time, var_name) pair
                    data_library[key].append((time_sd, data_val, data_sd))
    return weighted_sum, effective_weights_total, n_update, data_library # Return the updated values

sst_measurement_df = pd.read_csv("Modern case/measurement data/isla_senoritasst3_5_summary.csv")
sst_measurement_df.head()

# Calculate mean and std for each month across all years (skip 'Year' column)
mu_measurement_SST_monthly = sst_measurement_df.loc[:, sst_measurement_df.columns != 'Year'].mean(axis=0, skipna=True).values
std_measurement_SST_monthly = sst_measurement_df.loc[:, sst_measurement_df.columns != 'Year'].std(axis=0, skipna=True).values
print(mu_measurement_SST_monthly)
print(std_measurement_SST_monthly)

[26.05397715 22.93767813 22.17705242 25.16571014 27.72303465 28.34105633
 28.21574736 28.1912413  28.23161188 27.94042177 27.66587677 27.19749893]
[0.85420343 1.0662528  2.00874825 1.49485497 0.61468902 0.33940817
 0.30035706 0.29329485 0.28079002 0.33481732 0.46196816 0.73687447]

# Apply T47()-function from the D47calib package to all SST data
# Define a function to convert SST to D47 and also return the standard error
def sst_to_d47(sst):
    if pd.isna(sst):
        return pd.Series({'D47': np.nan, 'D47_SE': np.nan})
    d47, d47_se = D47c.OGLS23.T47(T = sst)
    return pd.Series({'D47': d47, 'D47_SE': d47_se})

# Apply the conversion to each month
month_abbr = ['ja', 'fb', 'mr', 'ar', 'my', 'jn', 'jl', 'ag', 'sp', 'ot', 'nv', 'dc']

# Create new columns for D47 and D47_SE
sst_measurement_D47_df = pd.DataFrame()
for month in month_abbr:
    sst_measurement_D47_df[[f'{month}_D47', f'{month}_D47_SE']] = sst_measurement_df[month].apply(sst_to_d47)
# Display the updated DataFrame
sst_measurement_D47_df.head()

# Calculate mean and std for each month across all years (skip 'Year' column)
mu_measurement_SST_D47_monthly = sst_measurement_D47_df[[f'{month}_D47' for month in month_abbr]].mean(axis=0, skipna=True).values
std_measurement_SST_D47_monthly = (
    sst_measurement_D47_df[[f'{month}_D47' for month in month_abbr]].std(axis=0, skipna=True).values ** 2 + # Standard deviation of the D47 values (squared to get variance)
    sst_measurement_D47_df[[f'{month}_D47_SE' for month in month_abbr]].mean(axis=0, skipna=True).values ** 2 # Standard error as estimate for the uncertainty in the calibration (squared to get variance)
) ** 0.5  # Combine variances and take square root to get standard deviation

print(mu_measurement_SST_D47_monthly)
print(std_measurement_SST_D47_monthly)

[0.59024743 0.5996984  0.60209239 0.59292986 0.58530679 0.58349698
 0.583862   0.58393343 0.58381556 0.58466662 0.58547229 0.58685417]
[0.00276576 0.00345025 0.00632303 0.00463432 0.00207955 0.00143587
 0.0013616  0.00134927 0.00132622 0.00143199 0.00171211 0.00242267]

# Load ESA SSS data as prior and show data structure
ESA_SSS = pd.read_csv('Modern case/SSS_Panama_all.csv')  # Load the data into Python and in the Jupyter environment.
# Convert 'timeseries' column to datetime
ESA_SSS['date'] = pd.to_datetime(ESA_SSS['date'], format='%Y%m%d')
# Rename longitude and latitude columns to 'lon' and 'lat'
ESA_SSS = ESA_SSS.rename(columns={'longitude': 'lon', 'latitude': 'lat'})

# Extract month as two-letter code
month_abbr = ['ja', 'fb', 'mr', 'ar', 'my', 'jn', 'jl', 'ag', 'sp', 'ot', 'nv', 'dc']
ESA_SSS['month'] = ESA_SSS['date'].dt.month.apply(lambda x: month_abbr[x-1])

# Group by lat, lon, and month, then calculate the mean salinity for each group
ESA_SSS = ESA_SSS.groupby(['lat', 'lon', 'month'], as_index=False)['salinity'].mean()

# Pivot to make one column per month, keeping all data
ESA_SSS = ESA_SSS.pivot(index=['lat', 'lon'], columns='month', values='salinity').reset_index()

ESA_SSS.head()

# Create list of month names
months = ['ja', 'fb', 'mr', 'ar', 'my', 'jn', 'jl', 'ag', 'sp', 'ot', 'nv', 'dc']

mu_measurement_SSS_monthly = np.array(ESA_SSS[[f"{month}" for month in months]].mean(axis=0, skipna=True))
cov_measurement_SSS_monthly = np.cov(ESA_SSS[[f"{month}" for month in months]].dropna(), rowvar=False)
std_measurement_SSS_monthly = np.sqrt(np.diag(cov_measurement_SSS_monthly))

# Define the seasons
seasons = {
    "winter": ["dc", "ja", "fb"],
    "spring": ["mr", "ar", "my"],
    "summer": ["jn", "jl", "ag"],
    "autumn": ["sp", "ot", "nv"],
}

mu_measurement_SSS_seasonal = np.array([ESA_SSS[seasons[season]].mean(axis=1, skipna=True).mean() for season in seasons])
cov_measurement_SSS_seasonal = np.cov([ESA_SSS[seasons[season]].mean(axis=1, skipna=True) for season in seasons], rowvar=True)
std_measurement_SSS_seasonal = np.sqrt(np.diag(cov_measurement_SSS_seasonal))

# Apply the d18Ow-SSS function from Graniero et al. (2017) to SSS data
# Identify the SSS columns
mu_measurement_d18Ow_monthly = -7.89 + 0.23 * mu_measurement_SSS_monthly.copy()
std_measurement_d18Ow_monthly = std_measurement_SSS_monthly.copy() * 0.23  # Convert SSS uncertainty to d18Ow uncertainty

print(mu_measurement_d18Ow_monthly)
print(std_measurement_d18Ow_monthly)

[-0.10042807  0.10322898  0.18594921  0.20426716  0.11048993 -0.03567929
 -0.11890993 -0.1688518  -0.24398497 -0.23124787 -0.30421288 -0.32621756]
[0.49096871 0.32583766 0.2580445  0.23462769 0.3023568  0.41988153
 0.48045419 0.5249147  0.58404172 0.62362581 0.67345612 0.6394892 ]

# Calculate d18Oc from SST and d18Ow using Grossman and Ku (1986) equation with updated d18Ow values
mu_measurement_d18Oc_monthly = (20.6 - mu_measurement_SST_monthly) / 4.34 + (mu_measurement_d18Ow_monthly - 0.27)
std_measurement_d18Oc_monthly = (
    (1 / 4.34) ** 2 * std_measurement_SST_monthly ** 2 +  # Variance from SST, corrected using the derivative of the d18Oc-temperature equation
    std_measurement_d18Ow_monthly ** 2  # Variance from d18Ow
) ** 0.5  # Combine variances and take square root to get standard deviation

print(mu_measurement_d18Oc_monthly)
print(std_measurement_d18Oc_monthly)

[-1.62710484 -0.70540653 -0.44742692 -1.11773979 -1.8007623  -2.08933282
 -2.14369043 -2.18798574 -2.27242089 -2.1925893  -2.20229508 -2.1163786 ]
[0.52895067 0.40807968 0.5299176  0.41675742 0.3338857  0.4271024
 0.48541302 0.52924704 0.58761431 0.62837949 0.68181635 0.6616449 ]

sat_measurement_df = pd.read_csv("Modern case/measurement data/culebra_SAT_summary.csv")
sat_measurement_df.head()

# Calculate mean and std for each month across all years (skip 'Year' column)
mu_measurement_SAT_monthly = sat_measurement_df.loc[:, sat_measurement_df.columns != 'Year'].mean(axis=0, skipna=True).values
std_measurement_SAT_monthly = sat_measurement_df.loc[:, sat_measurement_df.columns != 'Year'].std(axis=0, skipna=True).values
print(mu_measurement_SAT_monthly)
print(std_measurement_SAT_monthly)

[27.21333333 27.09333333 27.16       27.4        27.65333333 27.44666667
 27.30666667 27.24666667 27.22666667 27.03333333 26.64666667 27.09333333]
[0.54754865 0.46053799 0.52345009 0.4840307  0.35429339 0.44859569
 0.47429145 0.34819261 0.36735865 0.41518785 0.55660536 0.81544612]

precip_measurement_df = pd.read_csv("Modern case/measurement data/culebra_precip_summary.csv")
# Convert from mm/month to mm/day by dividing by the number of days per month
days_per_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
for i, col in enumerate(month_abbr):
    precip_measurement_df[col] = precip_measurement_df[col] / days_per_month[i]
precip_measurement_df.head()

# Calculate mean and std for each month across all years (skip 'Year' column)
mu_measurement_precip_monthly = precip_measurement_df.loc[:, precip_measurement_df.columns != 'Year'].mean(axis=0, skipna=True).values
std_measurement_precip_monthly = precip_measurement_df.loc[:, precip_measurement_df.columns != 'Year'].std(axis=0, skipna=True).values
print(mu_measurement_precip_monthly)
print(std_measurement_precip_monthly)

[0.83193548 0.24839286 0.67225806 1.649      5.48822581 6.66116667
 5.12903226 5.50230415 6.34936508 6.50076805 7.35904762 3.10875576]
[1.10390764 0.40655457 0.63890035 1.18891228 2.18837908 2.38718687
 2.5753094  2.89484492 2.61863124 1.68515274 2.42597887 1.91788101]

# Individual datapoints
mu_post_monthlySC, cov_post_monthlySC = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC = mu_post_monthlySC[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC = cov_post_monthlySC[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC = mu_post_monthlySC[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC = cov_post_monthlySC[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC = mu_post_monthlySC[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC = cov_post_monthlySC[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data
mu_post_monthly_aggregated, cov_post_monthly_aggregated = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated = mu_post_monthly_aggregated[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated = cov_post_monthly_aggregated[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated = mu_post_monthly_aggregated[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated = cov_post_monthly_aggregated[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated = mu_post_monthly_aggregated[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated = cov_post_monthly_aggregated[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# --- HIGHER UNCERTAINTY SCENARIOS ---
# Individual data with higher uncertainty on both D47 and d18O measurements
R_individual_HU = R_individual * 10  # Increase uncertainty by a factor of 10
mu_post_monthlySC_HU, cov_post_monthlySC_HU = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual_HU,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC_HU = mu_post_monthlySC_HU[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC_HU = cov_post_monthlySC_HU[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC_HU = mu_post_monthlySC_HU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC_HU = cov_post_monthlySC_HU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC_HU = mu_post_monthlySC_HU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC_HU = cov_post_monthlySC_HU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data with higher uncertainty on both D47 and d18O measurements
R_monthly_aggregated_HU = R_monthly_aggregated * 10  # Increase uncertainty by a factor of 10
mu_post_monthly_aggregated_HU, cov_post_monthly_aggregated_HU = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated_HU,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated_HU = mu_post_monthly_aggregated_HU[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated_HU = cov_post_monthly_aggregated_HU[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated_HU = mu_post_monthly_aggregated_HU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated_HU = cov_post_monthly_aggregated_HU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated_HU = mu_post_monthly_aggregated_HU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated_HU = cov_post_monthly_aggregated_HU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Individual data with higher uncertainty only on D47 measurements
R_individual_HU_D47 = R_individual.copy()
R_individual_HU_D47[:len(D47_measurement_uncertainties_individual), :len(D47_measurement_uncertainties_individual)] *= 10  # Increase uncertainty of D47 measurements by a factor of 10
mu_post_monthlySC_HU_D47, cov_post_monthlySC_HU_D47 = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual_HU_D47,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC_HU_D47 = mu_post_monthlySC_HU_D47[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC_HU_D47 = cov_post_monthlySC_HU_D47[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC_HU_D47 = mu_post_monthlySC_HU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC_HU_D47 = cov_post_monthlySC_HU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC_HU_D47 = mu_post_monthlySC_HU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC_HU_D47 = cov_post_monthlySC_HU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data with higher uncertainty only on D47 measurements
R_monthly_aggregated_HU_D47 = R_monthly_aggregated.copy()
R_monthly_aggregated_HU_D47[:len(D47_aggregated_uncertainties_monthly), :len(D47_aggregated_uncertainties_monthly)] *= 10  # Increase uncertainty of D47 measurements by a factor of 10

mu_post_monthly_aggregated_HU_D47, cov_post_monthly_aggregated_HU_D47 = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated_HU_D47,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated_HU_D47 = mu_post_monthly_aggregated_HU_D47[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated_HU_D47 = cov_post_monthly_aggregated_HU_D47[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated_HU_D47 = mu_post_monthly_aggregated_HU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated_HU_D47 = cov_post_monthly_aggregated_HU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated_HU_D47 = mu_post_monthly_aggregated_HU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated_HU_D47 = cov_post_monthly_aggregated_HU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Individual data with higher uncertainty only on d18Oc measurements
R_individual_HU_d18O = R_individual.copy()
R_individual_HU_d18O[len(D47_measurements_individual):, len(D47_measurements_individual):] *= 10  # Increase uncertainty of D47 measurements by a factor of 10
mu_post_monthlySC_HU_d18O, cov_post_monthlySC_HU_d18O = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual_HU_d18O,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC_HU_d18O = mu_post_monthlySC_HU_d18O[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC_HU_d18O = cov_post_monthlySC_HU_d18O[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC_HU_d18O = mu_post_monthlySC_HU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC_HU_d18O = cov_post_monthlySC_HU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC_HU_d18O = mu_post_monthlySC_HU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC_HU_d18O = cov_post_monthlySC_HU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data with higher uncertainty only on d18Oc measurements
R_monthly_aggregated_HU_d18O = R_monthly_aggregated.copy()
R_monthly_aggregated_HU_d18O[len(D47_aggregated_uncertainties_monthly):, len(D47_aggregated_uncertainties_monthly):] *= 10  # Increase uncertainty of D47 measurements by a factor of 10

mu_post_monthly_aggregated_HU_d18O, cov_post_monthly_aggregated_HU_d18O = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated_HU_d18O,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated_HU_d18O = mu_post_monthly_aggregated_HU_d18O[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated_HU_d18O = cov_post_monthly_aggregated_HU_d18O[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated_HU_d18O = mu_post_monthly_aggregated_HU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated_HU_d18O = cov_post_monthly_aggregated_HU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated_HU_d18O = mu_post_monthly_aggregated_HU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated_HU_d18O = cov_post_monthly_aggregated_HU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# --- LOWER UNCERTAINTY SCENARIOS ---
# Individual data with lower uncertainty on both D47 and d18O measurements
R_individual_LU = R_individual / 10  # Decrease uncertainty by a factor of 10
mu_post_monthlySC_LU, cov_post_monthlySC_LU = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual_LU,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC_LU = mu_post_monthlySC_LU[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC_LU = cov_post_monthlySC_LU[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC_LU = mu_post_monthlySC_LU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC_LU = cov_post_monthlySC_LU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC_LU = mu_post_monthlySC_LU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC_LU = cov_post_monthlySC_LU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data with lower uncertainty on both D47 and d18O measurements
R_monthly_aggregated_LU = R_monthly_aggregated / 10  # Decrease uncertainty by a factor of 10
mu_post_monthly_aggregated_LU, cov_post_monthly_aggregated_LU = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated_LU,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated_LU = mu_post_monthly_aggregated_LU[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated_LU = cov_post_monthly_aggregated_LU[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated_LU = mu_post_monthly_aggregated_LU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated_LU = cov_post_monthly_aggregated_LU[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated_LU = mu_post_monthly_aggregated_LU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated_LU = cov_post_monthly_aggregated_LU[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Individual data with lower uncertainty only on D47 measurements
R_individual_LU_D47 = R_individual.copy()
R_individual_LU_D47[:len(D47_measurement_uncertainties_individual), :len(D47_measurement_uncertainties_individual)] /= 10  # Decrease uncertainty of D47 measurements by a factor of 10
mu_post_monthlySC_LU_D47, cov_post_monthlySC_LU_D47 = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual_LU_D47,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC_LU_D47 = mu_post_monthlySC_LU_D47[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC_LU_D47 = cov_post_monthlySC_LU_D47[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC_LU_D47 = mu_post_monthlySC_LU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC_LU_D47 = cov_post_monthlySC_LU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC_LU_D47 = mu_post_monthlySC_LU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC_LU_D47 = cov_post_monthlySC_LU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data with lower uncertainty only on D47 measurements
R_monthly_aggregated_LU_D47 = R_monthly_aggregated.copy()
R_monthly_aggregated_LU_D47[:len(D47_aggregated_uncertainties_monthly), :len(D47_aggregated_uncertainties_monthly)] /= 10  # Decrease uncertainty of D47 measurements by a factor of 10
mu_post_monthly_aggregated_LU_D47, cov_post_monthly_aggregated_LU_D47 = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated_LU_D47,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated_LU_D47 = mu_post_monthly_aggregated_LU_D47[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated_LU_D47 = cov_post_monthly_aggregated_LU_D47[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated_LU_D47 = mu_post_monthly_aggregated_LU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated_LU_D47 = cov_post_monthly_aggregated_LU_D47[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated_LU_D47 = mu_post_monthly_aggregated_LU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated_LU_D47 = cov_post_monthly_aggregated_LU_D47[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Individual data with lower uncertainty only on d18Oc measurements
R_individual_LU_d18O = R_individual.copy()
R_individual_LU_d18O[len(D47_measurements_individual):, len(D47_measurements_individual):] /= 10  # Decrease uncertainty of D47 measurements by a factor of 10
mu_post_monthlySC_LU_d18O, cov_post_monthlySC_LU_d18O = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_individual,
    R_individual_LU_d18O,
    H_monthly
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthlySC_LU_d18O = mu_post_monthlySC_LU_d18O[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthlySC_LU_d18O = cov_post_monthlySC_LU_d18O[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthlySC_LU_d18O = mu_post_monthlySC_LU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthlySC_LU_d18O = cov_post_monthlySC_LU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthlySC_LU_d18O = mu_post_monthlySC_LU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthlySC_LU_d18O = cov_post_monthlySC_LU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Aggregated data with lower uncertainty only on d18Oc measurements
R_monthly_aggregated_LU_d18O = R_monthly_aggregated.copy()
R_monthly_aggregated_LU_d18O[len(D47_aggregated_uncertainties_monthly):, len(D47_aggregated_uncertainties_monthly):] /= 10  # Decrease uncertainty of D47 measurements by a factor of 10
mu_post_monthly_aggregated_LU_d18O, cov_post_monthly_aggregated_LU_d18O = kalman_update_block(
    mu_prior_monthly_combined,
    cov_prior_monthly_combined,
    Z_monthly_aggregated,
    R_monthly_aggregated_LU_d18O,
    H_monthly_aggregated
)
# Extract posterior means and covariance for SST D47
mu_post_SST_D47_monthly_aggregated_LU_d18O = mu_post_monthly_aggregated_LU_d18O[:len(mu_prior_SST_D47_monthly)]
cov_post_SST_D47_monthly_aggregated_LU_d18O = cov_post_monthly_aggregated_LU_d18O[:len(mu_prior_SST_D47_monthly), :len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for SAT D47
mu_post_SAT_D47_monthly_aggregated_LU_d18O = mu_post_monthly_aggregated_LU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
cov_post_SAT_D47_monthly_aggregated_LU_d18O = cov_post_monthly_aggregated_LU_d18O[len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly), len(mu_prior_SST_D47_monthly):2*len(mu_prior_SST_D47_monthly)]
# Extract posterior means and covariance for d18Oc
mu_post_d18Oc_monthly_aggregated_LU_d18O = mu_post_monthly_aggregated_LU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]
cov_post_d18Oc_monthly_aggregated_LU_d18O = cov_post_monthly_aggregated_LU_d18O[2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly), 2*len(mu_prior_d18Oc_monthly):3*len(mu_prior_d18Oc_monthly)]

# Prepare the data for the table
data = {
    "D47 data from:": [
        "In situ measurements",
        "Individual Measurements",
        "Individual Measurements (SD D47 * 10)",
        "Individual Measurements (SD d18Oc * 10)",
        "Individual Measurements (both SDs * 10)",
        "Individual Measurements (SD D47 * 0.1)",
        "Individual Measurements (SD d18Oc * 0.1)",
        "Individual Measurements (both SDs * 0.1)",
        "Aggregated Measurements",
        "Aggregated Measurements (SD D47 * 10)",
        "Aggregated Measurements (SD d18Oc * 10)",
        "Aggregated Measurements (both SDs * 10)",
        "Aggregated Measurements (SD D47 * 0.1)",
        "Aggregated Measurements (SD d18Oc * 0.1)",
        "Aggregated Measurements (both SDs * 0.1)"
    ]
}

# Add monthly means and standard deviations to the data dictionary
months = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"]

# Process and rename the means and standard deviations for each data source
D47_means_individual = mu_post_SST_D47_monthlySC
D47_stds_individual = np.sqrt(np.diag(cov_post_SST_D47_monthlySC))
D47_means_individual_hu_d47 = mu_post_SST_D47_monthlySC_HU_D47
D47_stds_individual_hu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU_D47))
D47_means_individual_hu_d18o = mu_post_SST_D47_monthlySC_HU_d18O
D47_stds_individual_hu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU_d18O))
D47_means_individual_hu = mu_post_SST_D47_monthlySC_HU
D47_stds_individual_hu = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU))
D47_means_individual_lu_d47 = mu_post_SST_D47_monthlySC_LU_D47
D47_stds_individual_lu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU_D47))
D47_means_individual_lu_d18o = mu_post_SST_D47_monthlySC_LU_d18O
D47_stds_individual_lu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU_d18O))
D47_means_individual_lu = mu_post_SST_D47_monthlySC_LU
D47_stds_individual_lu = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU))

D47_means_aggregated = mu_post_SST_D47_monthly_aggregated
D47_stds_aggregated = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated))
D47_means_aggregated_hu_d47 = mu_post_SST_D47_monthly_aggregated_HU_D47
D47_stds_aggregated_hu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU_D47))
D47_means_aggregated_hu_d18o = mu_post_SST_D47_monthly_aggregated_HU_d18O
D47_stds_aggregated_hu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU_d18O))
D47_means_aggregated_hu = mu_post_SST_D47_monthly_aggregated_HU
D47_stds_aggregated_hu = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU))
D47_means_aggregated_lu_d47 = mu_post_SST_D47_monthly_aggregated_LU_D47
D47_stds_aggregated_lu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU_D47))
D47_means_aggregated_lu_d18o = mu_post_SST_D47_monthly_aggregated_LU_d18O
D47_stds_aggregated_lu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU_d18O))
D47_means_aggregated_lu = mu_post_SST_D47_monthly_aggregated_LU
D47_stds_aggregated_lu = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU))

# Combine all means and standard deviations into the data structure
all_D47_means = [
    mu_measurement_SST_D47_monthly,
    D47_means_individual,
    D47_means_individual_hu_d47,
    D47_means_individual_hu_d18o,
    D47_means_individual_hu,
    D47_means_individual_lu_d47,
    D47_means_individual_lu_d18o,
    D47_means_individual_lu,
    D47_means_aggregated,
    D47_means_aggregated_hu_d47,
    D47_means_aggregated_hu_d18o,
    D47_means_aggregated_hu,
    D47_means_aggregated_lu_d47,
    D47_means_aggregated_lu_d18o,
    D47_means_aggregated_lu
]
all_D47_stds = [
    std_measurement_SST_D47_monthly,
    D47_stds_individual,
    D47_stds_individual_hu_d47,
    D47_stds_individual_hu_d18o,
    D47_stds_individual_hu,
    D47_stds_individual_lu_d47,
    D47_stds_individual_lu_d18o,
    D47_stds_individual_lu,
    D47_stds_aggregated,
    D47_stds_aggregated_hu_d47,
    D47_stds_aggregated_hu_d18o,
    D47_stds_aggregated_hu,
    D47_stds_aggregated_lu_d47,
    D47_stds_aggregated_lu_d18o,
    D47_stds_aggregated_lu
]

for i, month in enumerate(months):
    data[f"{month} Mean"] = [means[i] for means in all_D47_means]
    data[f"{month} Std"] = [stds[i] for stds in all_D47_stds]

# Create the Pandas DataFrame
D47_uncertainty_test_table_df = pd.DataFrame(data)

# Set the 'Data Type' column as the index
D47_uncertainty_test_table_df = D47_uncertainty_test_table_df.set_index("D47 data from:")

# Function to format mean and std
def format_mean_std(mean, std):
    return f"{mean:.4f} ± {std:.4f}"

# Apply the formatting function to the mean and std columns
for month in months:
    D47_uncertainty_test_table_df[month] = D47_uncertainty_test_table_df.apply(lambda row: format_mean_std(row[f"{month} Mean"], row[f"{month} Std"]), axis=1)
    D47_uncertainty_test_table_df = D47_uncertainty_test_table_df.drop(columns=[f"{month} Mean", f"{month} Std"])

# Print the table
print(D47_uncertainty_test_table_df.to_string())

# Export the table to a CSV file
D47_uncertainty_test_table_df.to_csv("Sensitivity_test_D47_d18Oc_uncertainties/D47_uncertainty_test_table.csv")

# Extract monthly means of measurements
mu_likelihood_monthly_D47 = Z_monthly_aggregated[:len(mu_prior_SST_D47_monthly)].flatten()
std_likelihood_monthly_D47 = np.sqrt(np.diag(R_monthly_aggregated))[:len(mu_prior_SST_D47_monthly)].flatten()

                                                  January         February            March            April              May             June             July           August        September          October         November         December
D47 data from:                                                                                                                                                                                                                                      
In situ measurements                      0.5902 ± 0.0028  0.5997 ± 0.0035  0.6021 ± 0.0063  0.5929 ± 0.0046  0.5853 ± 0.0021  0.5835 ± 0.0014  0.5839 ± 0.0014  0.5839 ± 0.0013  0.5838 ± 0.0013  0.5847 ± 0.0014  0.5855 ± 0.0017  0.5869 ± 0.0024
Individual Measurements                   0.5905 ± 0.0006  0.6069 ± 0.0005  0.6152 ± 0.0005  0.6103 ± 0.0005  0.5901 ± 0.0006  0.5749 ± 0.0006  0.5745 ± 0.0006  0.5731 ± 0.0006  0.5651 ± 0.0006  0.5590 ± 0.0006  0.5641 ± 0.0007  0.5742 ± 0.0006
Individual Measurements (SD D47 * 10)     0.5895 ± 0.0006  0.6061 ± 0.0005  0.6144 ± 0.0005  0.6095 ± 0.0005  0.5891 ± 0.0006  0.5738 ± 0.0006  0.5733 ± 0.0007  0.5720 ± 0.0007  0.5640 ± 0.0007  0.5580 ± 0.0006  0.5630 ± 0.0007  0.5730 ± 0.0007
Individual Measurements (SD d18Oc * 10)   0.5921 ± 0.0009  0.6000 ± 0.0008  0.6035 ± 0.0008  0.6000 ± 0.0008  0.5902 ± 0.0009  0.5838 ± 0.0010  0.5835 ± 0.0011  0.5825 ± 0.0011  0.5787 ± 0.0011  0.5761 ± 0.0010  0.5788 ± 0.0011  0.5841 ± 0.0011
Individual Measurements (both SDs * 10)   0.5891 ± 0.0010  0.5973 ± 0.0009  0.6009 ± 0.0009  0.5974 ± 0.0009  0.5872 ± 0.0010  0.5807 ± 0.0011  0.5802 ± 0.0011  0.5793 ± 0.0011  0.5757 ± 0.0011  0.5733 ± 0.0011  0.5757 ± 0.0012  0.5808 ± 0.0011
Individual Measurements (SD D47 * 0.1)    0.5968 ± 0.0005  0.6123 ± 0.0004  0.6199 ± 0.0004  0.6153 ± 0.0004  0.5964 ± 0.0005  0.5819 ± 0.0005  0.5817 ± 0.0005  0.5804 ± 0.0005  0.5721 ± 0.0005  0.5656 ± 0.0006  0.5714 ± 0.0006  0.5814 ± 0.0005
Individual Measurements (SD d18Oc * 0.1)  0.5727 ± 0.0003  0.6001 ± 0.0003  0.6149 ± 0.0003  0.6086 ± 0.0003  0.5753 ± 0.0003  0.5480 ± 0.0003  0.5462 ± 0.0004  0.5445 ± 0.0004  0.5333 ± 0.0003  0.5247 ± 0.0003  0.5308 ± 0.0004  0.5452 ± 0.0003
Individual Measurements (both SDs * 0.1)  0.5770 ± 0.0003  0.6038 ± 0.0003  0.6180 ± 0.0002  0.6119 ± 0.0003  0.5796 ± 0.0003  0.5529 ± 0.0003  0.5513 ± 0.0003  0.5497 ± 0.0003  0.5382 ± 0.0003  0.5294 ± 0.0003  0.5359 ± 0.0003  0.5502 ± 0.0003
Aggregated Measurements                   0.5856 ± 0.0012  0.5875 ± 0.0012  0.5880 ± 0.0012  0.5872 ± 0.0012  0.5853 ± 0.0011  0.5839 ± 0.0013  0.5832 ± 0.0014  0.5828 ± 0.0014  0.5820 ± 0.0014  0.5818 ± 0.0014  0.5821 ± 0.0014  0.5832 ± 0.0014
Aggregated Measurements (SD D47 * 10)     0.5854 ± 0.0012  0.5873 ± 0.0012  0.5879 ± 0.0012  0.5870 ± 0.0012  0.5851 ± 0.0011  0.5836 ± 0.0013  0.5830 ± 0.0014  0.5825 ± 0.0014  0.5817 ± 0.0014  0.5815 ± 0.0014  0.5818 ± 0.0015  0.5830 ± 0.0014
Aggregated Measurements (SD d18Oc * 10)   0.5859 ± 0.0013  0.5878 ± 0.0012  0.5881 ± 0.0013  0.5871 ± 0.0012  0.5853 ± 0.0012  0.5839 ± 0.0014  0.5833 ± 0.0015  0.5828 ± 0.0015  0.5821 ± 0.0015  0.5819 ± 0.0015  0.5823 ± 0.0016  0.5835 ± 0.0015
Aggregated Measurements (both SDs * 10)   0.5857 ± 0.0013  0.5876 ± 0.0012  0.5880 ± 0.0013  0.5869 ± 0.0012  0.5850 ± 0.0012  0.5837 ± 0.0014  0.5830 ± 0.0015  0.5825 ± 0.0015  0.5818 ± 0.0015  0.5817 ± 0.0015  0.5820 ± 0.0016  0.5832 ± 0.0015
Aggregated Measurements (SD D47 * 0.1)    0.5876 ± 0.0011  0.5891 ± 0.0011  0.5893 ± 0.0012  0.5885 ± 0.0012  0.5871 ± 0.0011  0.5861 ± 0.0012  0.5856 ± 0.0013  0.5852 ± 0.0013  0.5842 ± 0.0013  0.5839 ± 0.0013  0.5844 ± 0.0014  0.5856 ± 0.0013
Aggregated Measurements (SD d18Oc * 0.1)  0.5864 ± 0.0010  0.5896 ± 0.0010  0.5909 ± 0.0011  0.5901 ± 0.0010  0.5870 ± 0.0010  0.5835 ± 0.0010  0.5827 ± 0.0010  0.5824 ± 0.0011  0.5808 ± 0.0010  0.5800 ± 0.0010  0.5808 ± 0.0011  0.5826 ± 0.0010
Aggregated Measurements (both SDs * 0.1)  0.5877 ± 0.0009  0.5907 ± 0.0010  0.5919 ± 0.0010  0.5912 ± 0.0010  0.5882 ± 0.0009  0.5849 ± 0.0009  0.5842 ± 0.0010  0.5838 ± 0.0010  0.5822 ± 0.0010  0.5813 ± 0.0010  0.5822 ± 0.0010  0.5840 ± 0.0010

# Prepare the data for the table
data = {
    "d18Oc data from:": [
        "In situ measurements",
        "Individual Measurements",
        "Individual Measurements (SD D47 * 10)",
        "Individual Measurements (SD d18Oc * 10)",
        "Individual Measurements (both SDs * 10)",
        "Individual Measurements (SD D47 * 0.1)",
        "Individual Measurements (SD d18Oc * 0.1)",
        "Individual Measurements (both SDs * 0.1)",
        "Aggregated Measurements",
        "Aggregated Measurements (SD D47 * 10)",
        "Aggregated Measurements (SD d18Oc * 10)",
        "Aggregated Measurements (both SDs * 10)",
        "Aggregated Measurements (SD D47 * 0.1)",
        "Aggregated Measurements (SD d18Oc * 0.1)",
        "Aggregated Measurements (both SDs * 0.1)"
    ]
}

# Add monthly means and standard deviations to the data dictionary
months = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"]

# Process and rename the means and standard deviations for each data source
d18Oc_means_individual = mu_post_d18Oc_monthlySC
d18Oc_stds_individual = np.sqrt(np.diag(cov_post_d18Oc_monthlySC))
d18Oc_means_individual_hu_d47 = mu_post_d18Oc_monthlySC_HU_D47
d18Oc_stds_individual_hu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU_D47))
d18Oc_means_individual_hu_d18o = mu_post_d18Oc_monthlySC_HU_d18O
d18Oc_stds_individual_hu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU_d18O))
d18Oc_means_individual_hu = mu_post_d18Oc_monthlySC_HU
d18Oc_stds_individual_hu = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU))
d18Oc_means_individual_lu_d47 = mu_post_d18Oc_monthlySC_LU_D47
d18Oc_stds_individual_lu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU_D47))
d18Oc_means_individual_lu_d18o = mu_post_d18Oc_monthlySC_LU_d18O
d18Oc_stds_individual_lu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU_d18O))
d18Oc_means_individual_lu = mu_post_d18Oc_monthlySC_LU
d18Oc_stds_individual_lu = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU))

d18Oc_means_aggregated = mu_post_d18Oc_monthly_aggregated
d18Oc_stds_aggregated = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated))
d18Oc_means_aggregated_hu_d47 = mu_post_d18Oc_monthly_aggregated_HU_D47
d18Oc_stds_aggregated_hu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU_D47))
d18Oc_means_aggregated_hu_d18o = mu_post_d18Oc_monthly_aggregated_HU_d18O
d18Oc_stds_aggregated_hu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU_d18O))
d18Oc_means_aggregated_hu = mu_post_d18Oc_monthly_aggregated_HU
d18Oc_stds_aggregated_hu = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU))
d18Oc_means_aggregated_lu_d47 = mu_post_d18Oc_monthly_aggregated_LU_D47
d18Oc_stds_aggregated_lu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU_D47))
d18Oc_means_aggregated_lu_d18o = mu_post_d18Oc_monthly_aggregated_LU_d18O
d18Oc_stds_aggregated_lu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU_d18O))
d18Oc_means_aggregated_lu = mu_post_d18Oc_monthly_aggregated_LU
d18Oc_stds_aggregated_lu = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU))

# Combine all means and standard deviations into the data structure
all_d18Oc_means = [
    mu_measurement_d18Oc_monthly,
    d18Oc_means_individual,
    d18Oc_means_individual_hu_d47,
    d18Oc_means_individual_hu_d18o,
    d18Oc_means_individual_hu,
    d18Oc_means_individual_lu_d47,
    d18Oc_means_individual_lu_d18o,
    d18Oc_means_individual_lu,
    d18Oc_means_aggregated,
    d18Oc_means_aggregated_hu_d47,
    d18Oc_means_aggregated_hu_d18o,
    d18Oc_means_aggregated_hu,
    d18Oc_means_aggregated_lu_d47,
    d18Oc_means_aggregated_lu_d18o,
    d18Oc_means_aggregated_lu
]
all_d18Oc_stds = [
    std_measurement_d18Oc_monthly,
    d18Oc_stds_individual,
    d18Oc_stds_individual_hu_d47,
    d18Oc_stds_individual_hu_d18o,
    d18Oc_stds_individual_hu,
    d18Oc_stds_individual_lu_d47,
    d18Oc_stds_individual_lu_d18o,
    d18Oc_stds_individual_lu,
    d18Oc_stds_aggregated,
    d18Oc_stds_aggregated_hu_d47,
    d18Oc_stds_aggregated_hu_d18o,
    d18Oc_stds_aggregated_hu,
    d18Oc_stds_aggregated_lu_d47,
    d18Oc_stds_aggregated_lu_d18o,
    d18Oc_stds_aggregated_lu
]

for i, month in enumerate(months):
    data[f"{month} Mean"] = [means[i] for means in all_d18Oc_means]
    data[f"{month} Std"] = [stds[i] for stds in all_d18Oc_stds]

# Create the Pandas DataFrame
d18Oc_uncertainty_test_table_df = pd.DataFrame(data)

# Set the 'Data Type' column as the index
d18Oc_uncertainty_test_table_df = d18Oc_uncertainty_test_table_df.set_index("d18Oc data from:")

# Function to format mean and std
def format_mean_std(mean, std):
    return f"{mean:.3f} ± {std:.3f}"

# Apply the formatting function to the mean and std columns
for month in months:
    d18Oc_uncertainty_test_table_df[month] = d18Oc_uncertainty_test_table_df.apply(lambda row: format_mean_std(row[f"{month} Mean"], row[f"{month} Std"]), axis=1)
    d18Oc_uncertainty_test_table_df = d18Oc_uncertainty_test_table_df.drop(columns=[f"{month} Mean", f"{month} Std"])

# Print the table
print(d18Oc_uncertainty_test_table_df.to_string())

# Export the table to a CSV file
d18Oc_uncertainty_test_table_df.to_csv("Sensitivity_test_D47_d18Oc_uncertainties/d18Oc_uncertainty_test_table.csv")

# Extract monthly means of measurements
mu_likelihood_monthly_d18Oc = Z_monthly_aggregated[len(mu_prior_d18Oc_monthly):2*len(mu_prior_d18Oc_monthly)].flatten()
std_likelihood_monthly_d18Oc = np.sqrt(np.diag(R_monthly_aggregated))[len(mu_prior_d18Oc_monthly):2*len(mu_prior_d18Oc_monthly)].flatten()

                                                 January        February           March           April             May            June            July          August       September         October        November        December
d18Oc data from:                                                                                                                                                                                                                        
In situ measurements                      -1.627 ± 0.529  -0.705 ± 0.408  -0.447 ± 0.530  -1.118 ± 0.417  -1.801 ± 0.334  -2.089 ± 0.427  -2.144 ± 0.485  -2.188 ± 0.529  -2.272 ± 0.588  -2.193 ± 0.628  -2.202 ± 0.682  -2.116 ± 0.662
Individual Measurements                   -2.514 ± 0.007  -1.511 ± 0.006  -1.263 ± 0.006  -1.359 ± 0.008  -2.410 ± 0.011  -3.850 ± 0.012  -3.144 ± 0.018  -4.103 ± 0.016  -3.680 ± 0.015  -2.835 ± 0.014  -2.445 ± 0.013  -3.243 ± 0.010
Individual Measurements (SD D47 * 10)     -2.513 ± 0.008  -1.511 ± 0.006  -1.265 ± 0.006  -1.360 ± 0.008  -2.410 ± 0.011  -3.852 ± 0.012  -3.125 ± 0.018  -4.101 ± 0.016  -3.698 ± 0.015  -2.832 ± 0.014  -2.448 ± 0.013  -3.242 ± 0.010
Individual Measurements (SD d18Oc * 10)   -2.385 ± 0.020  -1.590 ± 0.016  -1.288 ± 0.016  -1.403 ± 0.021  -2.493 ± 0.032  -3.435 ± 0.029  -3.201 ± 0.041  -3.745 ± 0.040  -3.719 ± 0.033  -3.414 ± 0.032  -2.908 ± 0.032  -3.226 ± 0.029
Individual Measurements (both SDs * 10)   -2.379 ± 0.020  -1.592 ± 0.016  -1.294 ± 0.017  -1.411 ± 0.021  -2.497 ± 0.032  -3.432 ± 0.029  -3.117 ± 0.042  -3.730 ± 0.040  -3.774 ± 0.034  -3.400 ± 0.032  -2.925 ± 0.032  -3.228 ± 0.029
Individual Measurements (SD D47 * 0.1)    -2.520 ± 0.007  -1.512 ± 0.006  -1.255 ± 0.006  -1.350 ± 0.008  -2.412 ± 0.011  -3.832 ± 0.012  -3.266 ± 0.017  -4.111 ± 0.016  -3.570 ± 0.014  -2.859 ± 0.014  -2.428 ± 0.013  -3.250 ± 0.010
Individual Measurements (SD d18Oc * 0.1)  -2.688 ± 0.003  -1.342 ± 0.002  -1.263 ± 0.002  -1.557 ± 0.003  -2.260 ± 0.004  -3.826 ± 0.005  -3.303 ± 0.006  -4.224 ± 0.006  -3.910 ± 0.006  -2.378 ± 0.005  -2.259 ± 0.005  -3.212 ± 0.003
Individual Measurements (both SDs * 0.1)  -2.687 ± 0.003  -1.349 ± 0.002  -1.257 ± 0.002  -1.550 ± 0.003  -2.266 ± 0.003  -3.809 ± 0.005  -3.331 ± 0.006  -4.235 ± 0.006  -3.864 ± 0.005  -2.381 ± 0.005  -2.250 ± 0.005  -3.221 ± 0.003
Aggregated Measurements                   -2.747 ± 0.115  -2.452 ± 0.123  -2.274 ± 0.109  -2.469 ± 0.101  -2.909 ± 0.108  -3.278 ± 0.079  -3.099 ± 0.067  -3.072 ± 0.075  -3.060 ± 0.076  -2.894 ± 0.066  -2.844 ± 0.071  -2.851 ± 0.088
Aggregated Measurements (SD D47 * 10)     -2.747 ± 0.115  -2.451 ± 0.123  -2.274 ± 0.109  -2.471 ± 0.101  -2.914 ± 0.108  -3.281 ± 0.079  -3.092 ± 0.067  -3.072 ± 0.075  -3.065 ± 0.076  -2.892 ± 0.066  -2.844 ± 0.071  -2.853 ± 0.088
Aggregated Measurements (SD d18Oc * 10)   -2.508 ± 0.192  -2.068 ± 0.166  -1.900 ± 0.144  -2.004 ± 0.145  -2.512 ± 0.185  -2.958 ± 0.191  -2.958 ± 0.160  -3.051 ± 0.179  -3.209 ± 0.183  -3.183 ± 0.164  -3.085 ± 0.172  -2.981 ± 0.210
Aggregated Measurements (both SDs * 10)   -2.508 ± 0.192  -2.068 ± 0.166  -1.900 ± 0.144  -2.008 ± 0.145  -2.518 ± 0.185  -2.961 ± 0.191  -2.948 ± 0.161  -3.047 ± 0.179  -3.211 ± 0.183  -3.179 ± 0.164  -3.083 ± 0.172  -2.982 ± 0.210
Aggregated Measurements (SD D47 * 0.1)    -2.744 ± 0.115  -2.457 ± 0.123  -2.277 ± 0.109  -2.450 ± 0.101  -2.861 ± 0.108  -3.248 ± 0.078  -3.158 ± 0.065  -3.079 ± 0.075  -3.017 ± 0.076  -2.903 ± 0.066  -2.835 ± 0.071  -2.830 ± 0.088
Aggregated Measurements (SD d18Oc * 0.1)  -2.353 ± 0.073  -2.398 ± 0.082  -2.287 ± 0.068  -2.726 ± 0.060  -3.350 ± 0.077  -3.525 ± 0.030  -3.439 ± 0.032  -3.586 ± 0.036  -3.076 ± 0.037  -2.390 ± 0.026  -2.234 ± 0.037  -2.372 ± 0.051
Aggregated Measurements (both SDs * 0.1)  -2.356 ± 0.073  -2.398 ± 0.081  -2.286 ± 0.067  -2.715 ± 0.060  -3.332 ± 0.077  -3.517 ± 0.030  -3.465 ± 0.031  -3.579 ± 0.036  -3.045 ± 0.037  -2.393 ± 0.026  -2.226 ± 0.037  -2.371 ± 0.051

# Plot prior, likelihood and posterior distributions for D47 based on individual measurements

fig, axes = plt.subplots(4, 2, figsize=(20, 25))
fig.suptitle('Sensitivity Test: Effect of increased D47 and d18Oc Uncertainties on SST-D47', fontsize=24, fontweight='bold') # Provide title for the entire figure
plt.subplots_adjust(top=0.95) # Adjust top spacing to fit the title
plt.subplots_adjust(hspace=0.3) # Adjust vertical spacing between subplots to prevent overlap between titles and x-axis labels

# -- PANEL 1 -- DATA BASED ON INDIVIDUAL MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthlySC = np.sqrt(np.diag(cov_post_SST_D47_monthlySC))
std_prior_SST_D47_monthly_original = np.sqrt(np.diag(cov_prior_SST_D47_monthly_original))

# PRIOR
axes[0, 0].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 0].plot(months_scale, mu_post_SST_D47_monthlySC, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC - 2 * std_post_SST_D47_monthlySC,
    mu_post_SST_D47_monthlySC + 2 * std_post_SST_D47_monthlySC,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
# Set x-ticks and labels
axes[0, 0].set_xticks(months_scale)
axes[0, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 0].set_title('Based on individual measurements')
axes[0, 0].set_xlabel('Month')
axes[0, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[0, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[0, 0].legend()
axes[0, 0].grid(True)

# -- PANEL 2 -- DATA BASED ON AGGREGATED MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthly_aggregated = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated))

# PRIOR
axes[0, 1].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated - 2 * std_post_SST_D47_monthly_aggregated,
    mu_post_SST_D47_monthly_aggregated + 2 * std_post_SST_D47_monthly_aggregated,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[0, 1].set_xticks(months_scale)
axes[0, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 1].set_title('Based on aggregated measurements')
axes[0, 1].set_xlabel('Month')
axes[0, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[0, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[0, 1].legend()
axes[0, 1].grid(True)

# -- PANEL 3 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthlySC_HU = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU))

# PRIOR
axes[1, 0].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 0].plot(months_scale, mu_post_SST_D47_monthlySC_HU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC_HU - 2 * std_post_SST_D47_monthlySC_HU,
    mu_post_SST_D47_monthlySC_HU + 2 * std_post_SST_D47_monthlySC_HU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 0].set_xticks(months_scale)
axes[1, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 0].set_title('Based on individual measurements with 10x higher uncertainty in both D47 and d18Oc')
axes[1, 0].set_xlabel('Month')
axes[1, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[1, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[1, 0].legend()
axes[1, 0].grid(True)

# -- PANEL 4 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthly_aggregated_HU = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU))

# PRIOR
axes[1, 1].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated_HU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated_HU - 2 * std_post_SST_D47_monthly_aggregated_HU,
    mu_post_SST_D47_monthly_aggregated_HU + 2 * std_post_SST_D47_monthly_aggregated_HU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 1].set_xticks(months_scale)
axes[1, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 1].set_title('Based on aggregated measurements with 10x higher uncertainty in both D47 and d18Oc')
axes[1, 1].set_xlabel('Month')
axes[1, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[1, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[1, 1].legend()
axes[1, 1].grid(True)

# -- PANEL 5 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthlySC_HU_D47 = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU_D47))

# PRIOR
axes[2, 0].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 0].plot(months_scale, mu_post_SST_D47_monthlySC_HU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC_HU_D47 - 2 * std_post_SST_D47_monthlySC_HU_D47,
    mu_post_SST_D47_monthlySC_HU_D47 + 2 * std_post_SST_D47_monthlySC_HU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 0].set_xticks(months_scale)
axes[2, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 0].set_title('Based on individual measurements with 10x higher uncertainty in D47 only')
axes[2, 0].set_xlabel('Month')
axes[2, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[2, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[2, 0].legend()
axes[2, 0].grid(True)

# -- PANEL 6 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthly_aggregated_HU_D47 = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU_D47))

# PRIOR
axes[2, 1].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated_HU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated_HU_D47 - 2 * std_post_SST_D47_monthly_aggregated_HU_D47,
    mu_post_SST_D47_monthly_aggregated_HU_D47 + 2 * std_post_SST_D47_monthly_aggregated_HU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 1].set_xticks(months_scale)
axes[2, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 1].set_title('Based on aggregated measurements with 10x higher uncertainty in D47 only')
axes[2, 1].set_xlabel('Month')
axes[2, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[2, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[2, 1].legend()
axes[2, 1].grid(True)

# -- PANEL 7 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_SST_D47_monthlySC_HU_d18O = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU_d18O))

# PRIOR
axes[3, 0].plot(months_scale, mu_prior_SST_D47_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly - 2 * std_prior_SST_D47_monthly,
    mu_prior_SST_D47_monthly + 2 * std_prior_SST_D47_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 0].plot(months_scale, mu_post_SST_D47_monthlySC_HU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC_HU_d18O - 2 * std_post_SST_D47_monthlySC_HU_d18O,
    mu_post_SST_D47_monthlySC_HU_d18O + 2 * std_post_SST_D47_monthlySC_HU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 0].set_xticks(months_scale)
axes[3, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 0].set_title('Based on individual measurements with 10x higher uncertainty in d18Oc only')
axes[3, 0].set_xlabel('Month')
axes[3, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[3, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[3, 0].legend()
axes[3, 0].grid(True)

# -- PANEL 8 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_SST_D47_monthly_aggregated_HU_d18O = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU_d18O))

# PRIOR
axes[3, 1].plot(months_scale, mu_prior_SST_D47_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly - 2 * std_prior_SST_D47_monthly,
    mu_prior_SST_D47_monthly + 2 * std_prior_SST_D47_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated_HU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated_HU_d18O - 2 * std_post_SST_D47_monthly_aggregated_HU_d18O,
    mu_post_SST_D47_monthly_aggregated_HU_d18O + 2 * std_post_SST_D47_monthly_aggregated_HU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 1].set_xticks(months_scale)
axes[3, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 1].set_title('Based on aggregated measurements with 10x higher uncertainty in d18Oc only')
axes[3, 1].set_xlabel('Month')
axes[3, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[3, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[3, 1].legend()
axes[3, 1].grid(True)

# Show plot
plt.show()

# Plot prior, likelihood and posterior distributions for D47 based on individual measurements

fig, axes = plt.subplots(4, 2, figsize=(20, 25))
fig.suptitle('Sensitivity Test: Effect of reduced D47 and d18Oc Uncertainties on SST-D47', fontsize=24, fontweight='bold') # Provide title for the entire figure
plt.subplots_adjust(top=0.95) # Adjust top spacing to fit the title
plt.subplots_adjust(hspace=0.3) # Adjust vertical spacing between subplots to prevent overlap between titles and x-axis labels

# -- PANEL 1 -- DATA BASED ON INDIVIDUAL MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthlySC = np.sqrt(np.diag(cov_post_SST_D47_monthlySC))
std_prior_SST_D47_monthly_original = np.sqrt(np.diag(cov_prior_SST_D47_monthly_original))

# PRIOR
axes[0, 0].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 0].plot(months_scale, mu_post_SST_D47_monthlySC, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC - 2 * std_post_SST_D47_monthlySC,
    mu_post_SST_D47_monthlySC + 2 * std_post_SST_D47_monthlySC,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
# Set x-ticks and labels
axes[0, 0].set_xticks(months_scale)
axes[0, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 0].set_title('Based on individual measurements')
axes[0, 0].set_xlabel('Month')
axes[0, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[0, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[0, 0].legend()
axes[0, 0].grid(True)

# -- PANEL 2 -- DATA BASED ON AGGREGATED MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthly_aggregated = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated))

# PRIOR
axes[0, 1].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated - 2 * std_post_SST_D47_monthly_aggregated,
    mu_post_SST_D47_monthly_aggregated + 2 * std_post_SST_D47_monthly_aggregated,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[0, 1].set_xticks(months_scale)
axes[0, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 1].set_title('Based on aggregated measurements')
axes[0, 1].set_xlabel('Month')
axes[0, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[0, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[0, 1].legend()
axes[0, 1].grid(True)

# -- PANEL 3 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthlySC_LU = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU))

# PRIOR
axes[1, 0].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 0].plot(months_scale, mu_post_SST_D47_monthlySC_LU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC_LU - 2 * std_post_SST_D47_monthlySC_LU,
    mu_post_SST_D47_monthlySC_LU + 2 * std_post_SST_D47_monthlySC_LU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 0].set_xticks(months_scale)
axes[1, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 0].set_title('Based on individual measurements with 10x lower uncertainty in both D47 and d18Oc')
axes[1, 0].set_xlabel('Month')
axes[1, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[1, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[1, 0].legend()
axes[1, 0].grid(True)

# -- PANEL 4 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthly_aggregated_LU = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU))

# PRIOR
axes[1, 1].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated_LU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated_LU - 2 * std_post_SST_D47_monthly_aggregated_LU,
    mu_post_SST_D47_monthly_aggregated_LU + 2 * std_post_SST_D47_monthly_aggregated_LU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 1].set_xticks(months_scale)
axes[1, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 1].set_title('Based on aggregated measurements with 10x lower uncertainty in both D47 and d18Oc')
axes[1, 1].set_xlabel('Month')
axes[1, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[1, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[1, 1].legend()
axes[1, 1].grid(True)

# -- PANEL 5 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthlySC_LU_D47 = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU_D47))

# PRIOR
axes[2, 0].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 0].plot(months_scale, mu_post_SST_D47_monthlySC_LU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC_LU_D47 - 2 * std_post_SST_D47_monthlySC_LU_D47,
    mu_post_SST_D47_monthlySC_LU_D47 + 2 * std_post_SST_D47_monthlySC_LU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 0].set_xticks(months_scale)
axes[2, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 0].set_title('Based on individual measurements with 10x lower uncertainty in D47 only')
axes[2, 0].set_xlabel('Month')
axes[2, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[2, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[2, 0].legend()
axes[2, 0].grid(True)

# -- PANEL 6 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_SST_D47_monthly_aggregated_LU_D47 = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU_D47))

# PRIOR
axes[2, 1].plot(months_scale, mu_prior_SST_D47_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly_original - 2 * std_prior_SST_D47_monthly_original,
    mu_prior_SST_D47_monthly_original + 2 * std_prior_SST_D47_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated_LU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated_LU_D47 - 2 * std_post_SST_D47_monthly_aggregated_LU_D47,
    mu_post_SST_D47_monthly_aggregated_LU_D47 + 2 * std_post_SST_D47_monthly_aggregated_LU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 1].set_xticks(months_scale)
axes[2, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 1].set_title('Based on aggregated measurements with 10x lower uncertainty in D47 only')
axes[2, 1].set_xlabel('Month')
axes[2, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[2, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[2, 1].legend()
axes[2, 1].grid(True)

# -- PANEL 7 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_SST_D47_monthlySC_LU_d18O = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU_d18O))

# PRIOR
axes[3, 0].plot(months_scale, mu_prior_SST_D47_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly - 2 * std_prior_SST_D47_monthly,
    mu_prior_SST_D47_monthly + 2 * std_prior_SST_D47_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 0].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 0].plot(months_scale, mu_post_SST_D47_monthlySC_LU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_post_SST_D47_monthlySC_LU_d18O - 2 * std_post_SST_D47_monthlySC_LU_d18O,
    mu_post_SST_D47_monthlySC_LU_d18O + 2 * std_post_SST_D47_monthlySC_LU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 0].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 0].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 0].set_xticks(months_scale)
axes[3, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 0].set_title('Based on individual measurements with 10x lower uncertainty in d18Oc only')
axes[3, 0].set_xlabel('Month')
axes[3, 0].set_ylabel('SST-D47 value (I-CDES)')
axes[3, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[3, 0].legend()
axes[3, 0].grid(True)

# -- PANEL 8 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_SST_D47_monthly_aggregated_LU_d18O = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU_d18O))

# PRIOR
axes[3, 1].plot(months_scale, mu_prior_SST_D47_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_prior_SST_D47_monthly - 2 * std_prior_SST_D47_monthly,
    mu_prior_SST_D47_monthly + 2 * std_prior_SST_D47_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 1].plot(months_scale, mu_likelihood_monthly_D47, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_D47 - 2 * std_likelihood_monthly_D47,
    mu_likelihood_monthly_D47 + 2 * std_likelihood_monthly_D47,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 1].plot(months_scale, mu_post_SST_D47_monthly_aggregated_LU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_post_SST_D47_monthly_aggregated_LU_d18O - 2 * std_post_SST_D47_monthly_aggregated_LU_d18O,
    mu_post_SST_D47_monthly_aggregated_LU_d18O + 2 * std_post_SST_D47_monthly_aggregated_LU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 1].plot(months_scale, mu_measurement_SST_D47_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 1].fill_between(
    months_scale,
    mu_measurement_SST_D47_monthly - 2 * std_measurement_SST_D47_monthly,
    mu_measurement_SST_D47_monthly + 2 * std_measurement_SST_D47_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 1].set_xticks(months_scale)
axes[3, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 1].set_title('Based on aggregated measurements with 10x lower uncertainty in d18Oc only')
axes[3, 1].set_xlabel('Month')
axes[3, 1].set_ylabel('SST-D47 value (I-CDES)')
axes[3, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[3, 1].legend()
axes[3, 1].grid(True)

# Show plot
plt.show()

# Plot prior, likelihood and posterior distributions for D47 based on individual measurements

fig, axes = plt.subplots(4, 2, figsize=(20, 25))
fig.suptitle('Sensitivity Test: Effect of increased D47 and d18Oc Uncertainties on d18Oc', fontsize=24, fontweight='bold') # Provide title for the entire figure
plt.subplots_adjust(top=0.95) # Adjust top spacing to fit the title
plt.subplots_adjust(hspace=0.3) # Adjust vertical spacing between subplots to prevent overlap between titles and x-axis labels

# -- PANEL 1 -- DATA BASED ON INDIVIDUAL MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthlySC = np.sqrt(np.diag(cov_post_d18Oc_monthlySC))
std_prior_d18Oc_monthly_original = np.sqrt(np.diag(cov_prior_d18Oc_monthly_original))

# PRIOR
axes[0, 0].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 0].plot(months_scale, mu_post_d18Oc_monthlySC, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC - 2 * std_post_d18Oc_monthlySC,
    mu_post_d18Oc_monthlySC + 2 * std_post_d18Oc_monthlySC,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
# Set x-ticks and labels
axes[0, 0].set_xticks(months_scale)
axes[0, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 0].set_title('Based on individual measurements')
axes[0, 0].set_xlabel('Month')
axes[0, 0].set_ylabel('d18Oc value (VPDB)')
# axes[0, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[0, 0].legend()
axes[0, 0].grid(True)

# -- PANEL 2 -- DATA BASED ON AGGREGATED MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthly_aggregated = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated))

# PRIOR
axes[0, 1].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated - 2 * std_post_d18Oc_monthly_aggregated,
    mu_post_d18Oc_monthly_aggregated + 2 * std_post_d18Oc_monthly_aggregated,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[0, 1].set_xticks(months_scale)
axes[0, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 1].set_title('Based on aggregated measurements')
axes[0, 1].set_xlabel('Month')
axes[0, 1].set_ylabel('d18Oc value (VPDB)')
# axes[0, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[0, 1].legend()
axes[0, 1].grid(True)

# -- PANEL 3 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthlySC_HU = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU))

# PRIOR
axes[1, 0].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 0].plot(months_scale, mu_post_d18Oc_monthlySC_HU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC_HU - 2 * std_post_d18Oc_monthlySC_HU,
    mu_post_d18Oc_monthlySC_HU + 2 * std_post_d18Oc_monthlySC_HU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 0].set_xticks(months_scale)
axes[1, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 0].set_title('Based on individual measurements with 10x higher uncertainty in both D47 and d18Oc')
axes[1, 0].set_xlabel('Month')
axes[1, 0].set_ylabel('d18Oc value (VPDB)')
# axes[1, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[1, 0].legend()
axes[1, 0].grid(True)

# -- PANEL 4 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthly_aggregated_HU = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU))

# PRIOR
axes[1, 1].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated_HU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated_HU - 2 * std_post_d18Oc_monthly_aggregated_HU,
    mu_post_d18Oc_monthly_aggregated_HU + 2 * std_post_d18Oc_monthly_aggregated_HU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 1].set_xticks(months_scale)
axes[1, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 1].set_title('Based on aggregated measurements with 10x higher uncertainty in both D47 and d18Oc')
axes[1, 1].set_xlabel('Month')
axes[1, 1].set_ylabel('d18Oc value (VPDB)')
# axes[1, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[1, 1].legend()
axes[1, 1].grid(True)

# -- PANEL 5 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthlySC_HU_D47 = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU_D47))

# PRIOR
axes[2, 0].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 0].plot(months_scale, mu_post_d18Oc_monthlySC_HU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC_HU_D47 - 2 * std_post_d18Oc_monthlySC_HU_D47,
    mu_post_d18Oc_monthlySC_HU_D47 + 2 * std_post_d18Oc_monthlySC_HU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 0].set_xticks(months_scale)
axes[2, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 0].set_title('Based on individual measurements with 10x higher uncertainty in D47 only')
axes[2, 0].set_xlabel('Month')
axes[2, 0].set_ylabel('d18Oc value (VPDB)')
# axes[2, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[2, 0].legend()
axes[2, 0].grid(True)

# -- PANEL 6 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthly_aggregated_HU_D47 = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU_D47))

# PRIOR
axes[2, 1].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated_HU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated_HU_D47 - 2 * std_post_d18Oc_monthly_aggregated_HU_D47,
    mu_post_d18Oc_monthly_aggregated_HU_D47 + 2 * std_post_d18Oc_monthly_aggregated_HU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 1].set_xticks(months_scale)
axes[2, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 1].set_title('Based on aggregated measurements with 10x higher uncertainty in D47 only')
axes[2, 1].set_xlabel('Month')
axes[2, 1].set_ylabel('d18Oc value (VPDB)')
# axes[2, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[2, 1].legend()
axes[2, 1].grid(True)

# -- PANEL 7 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_d18Oc_monthlySC_HU_d18O = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU_d18O))

# PRIOR
axes[3, 0].plot(months_scale, mu_prior_d18Oc_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly - 2 * std_prior_d18Oc_monthly,
    mu_prior_d18Oc_monthly + 2 * std_prior_d18Oc_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 0].plot(months_scale, mu_post_d18Oc_monthlySC_HU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC_HU_d18O - 2 * std_post_d18Oc_monthlySC_HU_d18O,
    mu_post_d18Oc_monthlySC_HU_d18O + 2 * std_post_d18Oc_monthlySC_HU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 0].set_xticks(months_scale)
axes[3, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 0].set_title('Based on individual measurements with 10x higher uncertainty in d18Oc only')
axes[3, 0].set_xlabel('Month')
axes[3, 0].set_ylabel('d18Oc value (VPDB)')
# axes[3, 0].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[3, 0].legend()
axes[3, 0].grid(True)

# -- PANEL 8 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_d18Oc_monthly_aggregated_HU_d18O = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU_d18O))

# PRIOR
axes[3, 1].plot(months_scale, mu_prior_d18Oc_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly - 2 * std_prior_d18Oc_monthly,
    mu_prior_d18Oc_monthly + 2 * std_prior_d18Oc_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated_HU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated_HU_d18O - 2 * std_post_d18Oc_monthly_aggregated_HU_d18O,
    mu_post_d18Oc_monthly_aggregated_HU_d18O + 2 * std_post_d18Oc_monthly_aggregated_HU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 1].set_xticks(months_scale)
axes[3, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 1].set_title('Based on aggregated measurements with 10x higher uncertainty in d18Oc only')
axes[3, 1].set_xlabel('Month')
axes[3, 1].set_ylabel('d18Oc value (VPDB)')
# axes[3, 1].set_ylim(0.57, 0.63)  # Set y-axis limits for better visibility
axes[3, 1].legend()
axes[3, 1].grid(True)

# Show plot
plt.show()

# Plot prior, likelihood and posterior distributions for D47 based on individual measurements

fig, axes = plt.subplots(4, 2, figsize=(20, 25))
fig.suptitle('Sensitivity Test: Effect of reduced D47 and d18Oc Uncertainties on d18Oc', fontsize=24, fontweight='bold') # Provide title for the entire figure
plt.subplots_adjust(top=0.95) # Adjust top spacing to fit the title
plt.subplots_adjust(hspace=0.3) # Adjust vertical spacing between subplots to prevent overlap between titles and x-axis labels

# -- PANEL 1 -- DATA BASED ON INDIVIDUAL MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthlySC = np.sqrt(np.diag(cov_post_d18Oc_monthlySC))
std_prior_d18Oc_monthly_original = np.sqrt(np.diag(cov_prior_d18Oc_monthly_original))

# PRIOR
axes[0, 0].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 0].plot(months_scale, mu_post_d18Oc_monthlySC, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC - 2 * std_post_d18Oc_monthlySC,
    mu_post_d18Oc_monthlySC + 2 * std_post_d18Oc_monthlySC,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
# Set x-ticks and labels
axes[0, 0].set_xticks(months_scale)
axes[0, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 0].set_title('Based on individual measurements')
axes[0, 0].set_xlabel('Month')
axes[0, 0].set_ylabel('d18Oc value (VPDB)')
# axes[0, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[0, 0].legend()
axes[0, 0].grid(True)

# -- PANEL 2 -- DATA BASED ON AGGREGATED MEASUREMENTS
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthly_aggregated = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated))

# PRIOR
axes[0, 1].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[0, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[0, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[0, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated - 2 * std_post_d18Oc_monthly_aggregated,
    mu_post_d18Oc_monthly_aggregated + 2 * std_post_d18Oc_monthly_aggregated,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[0, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[0, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[0, 1].set_xticks(months_scale)
axes[0, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[0, 1].set_title('Based on aggregated measurements')
axes[0, 1].set_xlabel('Month')
axes[0, 1].set_ylabel('d18Oc value (VPDB)')
# axes[0, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[0, 1].legend()
axes[0, 1].grid(True)

# -- PANEL 3 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthlySC_LU = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU))

# PRIOR
axes[1, 0].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 0].plot(months_scale, mu_post_d18Oc_monthlySC_LU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC_LU - 2 * std_post_d18Oc_monthlySC_LU,
    mu_post_d18Oc_monthlySC_LU + 2 * std_post_d18Oc_monthlySC_LU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 0].set_xticks(months_scale)
axes[1, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 0].set_title('Based on individual measurements with 10x lower uncertainty in both D47 and d18Oc')
axes[1, 0].set_xlabel('Month')
axes[1, 0].set_ylabel('d18Oc value (VPDB)')
# axes[1, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[1, 0].legend()
axes[1, 0].grid(True)

# -- PANEL 4 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON BOTH D47 AND d18O
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthly_aggregated_LU = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU))

# PRIOR
axes[1, 1].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[1, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[1, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated_LU, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[1, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated_LU - 2 * std_post_d18Oc_monthly_aggregated_LU,
    mu_post_d18Oc_monthly_aggregated_LU + 2 * std_post_d18Oc_monthly_aggregated_LU,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[1, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[1, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[1, 1].set_xticks(months_scale)
axes[1, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[1, 1].set_title('Based on aggregated measurements with 10x lower uncertainty in both D47 and d18Oc')
axes[1, 1].set_xlabel('Month')
axes[1, 1].set_ylabel('d18Oc value (VPDB)')
# axes[1, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[1, 1].legend()
axes[1, 1].grid(True)

# -- PANEL 5 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthlySC_LU_D47 = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU_D47))

# PRIOR
axes[2, 0].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 0].plot(months_scale, mu_post_d18Oc_monthlySC_LU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC_LU_D47 - 2 * std_post_d18Oc_monthlySC_LU_D47,
    mu_post_d18Oc_monthlySC_LU_D47 + 2 * std_post_d18Oc_monthlySC_LU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 0].set_xticks(months_scale)
axes[2, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 0].set_title('Based on individual measurements with 10x lower uncertainty in D47 only')
axes[2, 0].set_xlabel('Month')
axes[2, 0].set_ylabel('d18Oc value (VPDB)')
# axes[2, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[2, 0].legend()
axes[2, 0].grid(True)

# -- PANEL 6 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON D47 ONLY
# Calculate the updated seasonal posterior for SST_D47
std_post_d18Oc_monthly_aggregated_LU_D47 = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU_D47))

# PRIOR
axes[2, 1].plot(months_scale, mu_prior_d18Oc_monthly_original, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly_original - 2 * std_prior_d18Oc_monthly_original,
    mu_prior_d18Oc_monthly_original + 2 * std_prior_d18Oc_monthly_original,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[2, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[2, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated_LU_D47, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[2, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated_LU_D47 - 2 * std_post_d18Oc_monthly_aggregated_LU_D47,
    mu_post_d18Oc_monthly_aggregated_LU_D47 + 2 * std_post_d18Oc_monthly_aggregated_LU_D47,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[2, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (SST)', color='b', marker='x')
axes[2, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[2, 1].set_xticks(months_scale)
axes[2, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[2, 1].set_title('Based on aggregated measurements with 10x lower uncertainty in D47 only')
axes[2, 1].set_xlabel('Month')
axes[2, 1].set_ylabel('d18Oc value (VPDB)')
# axes[2, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[2, 1].legend()
axes[2, 1].grid(True)

# -- PANEL 7 -- DATA BASED ON INDIVIDUAL MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_d18Oc_monthlySC_LU_d18O = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU_d18O))

# PRIOR
axes[3, 0].plot(months_scale, mu_prior_d18Oc_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly - 2 * std_prior_d18Oc_monthly,
    mu_prior_d18Oc_monthly + 2 * std_prior_d18Oc_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 0].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 0].plot(months_scale, mu_post_d18Oc_monthlySC_LU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 0].fill_between(
    months_scale,
    mu_post_d18Oc_monthlySC_LU_d18O - 2 * std_post_d18Oc_monthlySC_LU_d18O,
    mu_post_d18Oc_monthlySC_LU_d18O + 2 * std_post_d18Oc_monthlySC_LU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 0].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 0].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 0].set_xticks(months_scale)
axes[3, 0].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 0].set_title('Based on individual measurements with 10x lower uncertainty in d18Oc only')
axes[3, 0].set_xlabel('Month')
axes[3, 0].set_ylabel('d18Oc value (VPDB)')
# axes[3, 0].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[3, 0].legend()
axes[3, 0].grid(True)

# -- PANEL 8 -- DATA BASED ON AGGREGATED MEASUREMENTS WITH HIGHER UNCERTAINTY ON d18Oc ONLY
# Calculate the updated seasonal posterior for D47
std_post_d18Oc_monthly_aggregated_LU_d18O = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU_d18O))

# PRIOR
axes[3, 1].plot(months_scale, mu_prior_d18Oc_monthly, label='Prior Mean (IPCC_Atlas models)', color='g', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_prior_d18Oc_monthly - 2 * std_prior_d18Oc_monthly,
    mu_prior_d18Oc_monthly + 2 * std_prior_d18Oc_monthly,
    color='g',
    alpha=0.2,
    label='+/- 2 SD'
)
# LIKELIHOOD
axes[3, 1].plot(months_scale, mu_likelihood_monthly_d18Oc, label='Likelihood Mean (clumped data)', color='y', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_likelihood_monthly_d18Oc - 2 * std_likelihood_monthly_d18Oc,
    mu_likelihood_monthly_d18Oc + 2 * std_likelihood_monthly_d18Oc,
    color='y',
    alpha=0.2,
    label='+/- 2 SD'
)
# POSTERIOR
axes[3, 1].plot(months_scale, mu_post_d18Oc_monthly_aggregated_LU_d18O, label='Posterior Mean (IPCC_Atlas models + clumped data)', color='r', marker='o')
axes[3, 1].fill_between(
    months_scale,
    mu_post_d18Oc_monthly_aggregated_LU_d18O - 2 * std_post_d18Oc_monthly_aggregated_LU_d18O,
    mu_post_d18Oc_monthly_aggregated_LU_d18O + 2 * std_post_d18Oc_monthly_aggregated_LU_d18O,
    color='r',
    alpha=0.2,
    label='+/- 2 SD (Posterior)'
)
# MEASUREMENT DATA
axes[3, 1].plot(months_scale, mu_measurement_d18Oc_monthly, label='Measurement Mean (d18Oc)', color='b', marker='x')
axes[3, 1].fill_between(
    months_scale,
    mu_measurement_d18Oc_monthly - 2 * std_measurement_d18Oc_monthly,
    mu_measurement_d18Oc_monthly + 2 * std_measurement_d18Oc_monthly,
    color='b',
    alpha=0.2,
    label='+/- 2 SD (Measurements)'
)
axes[3, 1].set_xticks(months_scale)
axes[3, 1].set_xticklabels(month_names, rotation=45, ha="right")
axes[3, 1].set_title('Based on aggregated measurements with 10x lower uncertainty in d18Oc only')
axes[3, 1].set_xlabel('Month')
axes[3, 1].set_ylabel('d18Oc value (VPDB)')
# axes[3, 1].set_ylim(0.54, 0.63)  # Set y-axis limits for better visibility
axes[3, 1].legend()
axes[3, 1].grid(True)

# Show plot
plt.show()

# Prepare the data for the table
data = {
    "Data Type": [
        "Prior estimates",
        "In situ measurements",
        "Individual Measurements",
        "Individual Measurements (SD D47 * 10)",
        "Individual Measurements (SD d18Oc * 10)",
        "Individual Measurements (both SDs * 10)",
        "Individual Measurements (SD D47 * 0.1)",
        "Individual Measurements (SD d18Oc * 0.1)",
        "Individual Measurements (both SDs * 0.1)",
        "Aggregated Measurements",
        "Aggregated Measurements (SD D47 * 10)",
        "Aggregated Measurements (SD d18Oc * 10)",
        "Aggregated Measurements (both SDs * 10)",
        "Aggregated Measurements (SD D47 * 0.1)",
        "Aggregated Measurements (SD d18Oc * 0.1)",
        "Aggregated Measurements (both SDs * 0.1)"
    ]
}

# Add monthly means and standard deviations to the data dictionary
months = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"]

# Process and rename the means and standard deviations for each data source
D47_means_prior = mu_prior_SST_D47_monthly_original
D47_stds_prior = np.sqrt(np.diag(cov_prior_SST_D47_monthly_original))

D47_means_individual = mu_post_SST_D47_monthlySC
D47_stds_individual = np.sqrt(np.diag(cov_post_SST_D47_monthlySC))
D47_means_individual_hu_d47 = mu_post_SST_D47_monthlySC_HU_D47
D47_stds_individual_hu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU_D47))
D47_means_individual_hu_d18o = mu_post_SST_D47_monthlySC_HU_d18O
D47_stds_individual_hu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU_d18O))
D47_means_individual_hu = mu_post_SST_D47_monthlySC_HU
D47_stds_individual_hu = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_HU))
D47_means_individual_lu_d47 = mu_post_SST_D47_monthlySC_LU_D47
D47_stds_individual_lu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU_D47))
D47_means_individual_lu_d18o = mu_post_SST_D47_monthlySC_LU_d18O
D47_stds_individual_lu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU_d18O))
D47_means_individual_lu = mu_post_SST_D47_monthlySC_LU
D47_stds_individual_lu = np.sqrt(np.diag(cov_post_SST_D47_monthlySC_LU))

D47_means_aggregated = mu_post_SST_D47_monthly_aggregated
D47_stds_aggregated = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated))
D47_means_aggregated_hu_d47 = mu_post_SST_D47_monthly_aggregated_HU_D47
D47_stds_aggregated_hu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU_D47))
D47_means_aggregated_hu_d18o = mu_post_SST_D47_monthly_aggregated_HU_d18O
D47_stds_aggregated_hu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU_d18O))
D47_means_aggregated_hu = mu_post_SST_D47_monthly_aggregated_HU
D47_stds_aggregated_hu = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_HU))
D47_means_aggregated_lu_d47 = mu_post_SST_D47_monthly_aggregated_LU_D47
D47_stds_aggregated_lu_d47 = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU_D47))
D47_means_aggregated_lu_d18o = mu_post_SST_D47_monthly_aggregated_LU_d18O
D47_stds_aggregated_lu_d18o = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU_d18O))
D47_means_aggregated_lu = mu_post_SST_D47_monthly_aggregated_LU
D47_stds_aggregated_lu = np.sqrt(np.diag(cov_post_SST_D47_monthly_aggregated_LU))

d18Oc_means_prior = mu_prior_d18Oc_monthly_original
d18Oc_stds_prior = np.sqrt(np.diag(cov_prior_d18Oc_monthly_original))

d18Oc_means_individual = mu_post_d18Oc_monthlySC
d18Oc_stds_individual = np.sqrt(np.diag(cov_post_d18Oc_monthlySC))
d18Oc_means_individual_hu_d47 = mu_post_d18Oc_monthlySC_HU_D47
d18Oc_stds_individual_hu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU_D47))
d18Oc_means_individual_hu_d18o = mu_post_d18Oc_monthlySC_HU_d18O
d18Oc_stds_individual_hu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU_d18O))
d18Oc_means_individual_hu = mu_post_d18Oc_monthlySC_HU
d18Oc_stds_individual_hu = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_HU))
d18Oc_means_individual_lu_d47 = mu_post_d18Oc_monthlySC_LU_D47
d18Oc_stds_individual_lu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU_D47))
d18Oc_means_individual_lu_d18o = mu_post_d18Oc_monthlySC_LU_d18O
d18Oc_stds_individual_lu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU_d18O))
d18Oc_means_individual_lu = mu_post_d18Oc_monthlySC_LU
d18Oc_stds_individual_lu = np.sqrt(np.diag(cov_post_d18Oc_monthlySC_LU))

d18Oc_means_aggregated = mu_post_d18Oc_monthly_aggregated
d18Oc_stds_aggregated = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated))
d18Oc_means_aggregated_hu_d47 = mu_post_d18Oc_monthly_aggregated_HU_D47
d18Oc_stds_aggregated_hu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU_D47))
d18Oc_means_aggregated_hu_d18o = mu_post_d18Oc_monthly_aggregated_HU_d18O
d18Oc_stds_aggregated_hu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU_d18O))
d18Oc_means_aggregated_hu = mu_post_d18Oc_monthly_aggregated_HU
d18Oc_stds_aggregated_hu = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_HU))
d18Oc_means_aggregated_lu_d47 = mu_post_d18Oc_monthly_aggregated_LU_D47
d18Oc_stds_aggregated_lu_d47 = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU_D47))
d18Oc_means_aggregated_lu_d18o = mu_post_d18Oc_monthly_aggregated_LU_d18O
d18Oc_stds_aggregated_lu_d18o = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU_d18O))
d18Oc_means_aggregated_lu = mu_post_d18Oc_monthly_aggregated_LU
d18Oc_stds_aggregated_lu = np.sqrt(np.diag(cov_post_d18Oc_monthly_aggregated_LU))

# Combine all means and standard deviations into the data structure
all_D47_means = [
    D47_means_prior,
    mu_measurement_SST_D47_monthly,
    D47_means_individual,
    D47_means_individual_hu_d47,
    D47_means_individual_hu_d18o,
    D47_means_individual_hu,
    D47_means_individual_lu_d47,
    D47_means_individual_lu_d18o,
    D47_means_individual_lu,
    D47_means_aggregated,
    D47_means_aggregated_hu_d47,
    D47_means_aggregated_hu_d18o,
    D47_means_aggregated_hu,
    D47_means_aggregated_lu_d47,
    D47_means_aggregated_lu_d18o,
    D47_means_aggregated_lu
]
all_D47_stds = [
    D47_stds_prior,
    std_measurement_SST_D47_monthly,
    D47_stds_individual,
    D47_stds_individual_hu_d47,
    D47_stds_individual_hu_d18o,
    D47_stds_individual_hu,
    D47_stds_individual_lu_d47,
    D47_stds_individual_lu_d18o,
    D47_stds_individual_lu,
    D47_stds_aggregated,
    D47_stds_aggregated_hu_d47,
    D47_stds_aggregated_hu_d18o,
    D47_stds_aggregated_hu,
    D47_stds_aggregated_lu_d47,
    D47_stds_aggregated_lu_d18o,
    D47_stds_aggregated_lu
]

all_d18Oc_means = [
    d18Oc_means_prior,
    mu_measurement_d18Oc_monthly,
    d18Oc_means_individual,
    d18Oc_means_individual_hu_d47,
    d18Oc_means_individual_hu_d18o,
    d18Oc_means_individual_hu,
    d18Oc_means_individual_lu_d47,
    d18Oc_means_individual_lu_d18o,
    d18Oc_means_individual_lu,
    d18Oc_means_aggregated,
    d18Oc_means_aggregated_hu_d47,
    d18Oc_means_aggregated_hu_d18o,
    d18Oc_means_aggregated_hu,
    d18Oc_means_aggregated_lu_d47,
    d18Oc_means_aggregated_lu_d18o,
    d18Oc_means_aggregated_lu
]
all_d18Oc_stds = [
    d18Oc_stds_prior,
    std_measurement_d18Oc_monthly,
    d18Oc_stds_individual,
    d18Oc_stds_individual_hu_d47,
    d18Oc_stds_individual_hu_d18o,
    d18Oc_stds_individual_hu,
    d18Oc_stds_individual_lu_d47,
    d18Oc_stds_individual_lu_d18o,
    d18Oc_stds_individual_lu,
    d18Oc_stds_aggregated,
    d18Oc_stds_aggregated_hu_d47,
    d18Oc_stds_aggregated_hu_d18o,
    d18Oc_stds_aggregated_hu,
    d18Oc_stds_aggregated_lu_d47,
    d18Oc_stds_aggregated_lu_d18o,
    d18Oc_stds_aggregated_lu
]

# Create a dictionary to store all the data
all_data = {"Data Type": data["Data Type"]}

# Add D47 means and stds
for i, month in enumerate(months):
    all_data[f"{month} D47 Mean"] = [means[i] for means in all_D47_means]
    all_data[f"{month} D47 Std"] = [stds[i] for stds in all_D47_stds]

# Add d18Oc means and stds
for i, month in enumerate(months):
    all_data[f"{month} d18Oc Mean"] = [means[i] for means in all_d18Oc_means]
    all_data[f"{month} d18Oc Std"] = [stds[i] for stds in all_d18Oc_stds]

# Create the Pandas DataFrame
all_uncertainty_test_table_df = pd.DataFrame(all_data)

# Set the 'Data Type' column as the index
all_uncertainty_test_table_df = all_uncertainty_test_table_df.set_index("Data Type")

# Export the table to a CSV file
all_uncertainty_test_table_df.to_csv("Sensitivity_test_D47_d18Oc_uncertainties/all_uncertainty_test_table.csv")

print("Combined data exported to Sensitivity_test_D47_d18Oc_uncertainties/all_uncertainty_test_table.csv")

Combined data exported to Sensitivity_test_D47_d18Oc_uncertainties/all_uncertainty_test_table.csv

# Calculate accuracy of monthly D47 and d18Oc from difference between mean and measurement mean
accuracy_D47 = all_uncertainty_test_table_df.filter(like='D47 Mean').subtract(mu_measurement_SST_D47_monthly).abs()
accuracy_d18Oc = all_uncertainty_test_table_df.filter(like='d18Oc Mean').subtract(mu_measurement_d18Oc_monthly).abs()

# Calculate precision of monthly D47 and d18Oc from standard deviation
precision_D47 = all_uncertainty_test_table_df.filter(like='D47 Std')
precision_d18Oc = all_uncertainty_test_table_df.filter(like='d18Oc Std')

fig, ((ax2, ax4), (ax1, ax3)) = plt.subplots(
    2, 2, figsize=(18, 12), sharex='col'
)
fig.subplots_adjust(hspace=0.1, wspace=0.25)  # reduce vertical & horizontal spacing

# Define a colormap across all months
cmap = plt.cm.coolwarm
colors = [cmap(i / (len(months)-1)) for i in range(len(months))]
color_dict = dict(zip(months, colors))

# ---------------------------------------------------------
# --- Accuracy Plot (Bottom Left: D47) ---
for month in months:
    ax1.scatter(accuracy_D47.index, accuracy_D47[f"{month} D47 Mean"], s=20, label=month, color=color_dict[month])

ax1.set_xticks(accuracy_D47.index)
ax1.set_xticklabels(accuracy_D47.index, rotation=45, ha="right")
ax1.set_xlabel('Data Type')
ax1.set_ylabel('D47 Accuracy (‰ I-CDES)\n(Abs. Difference from Measurement Mean)', color='blue')
ax1.tick_params(axis='y', labelcolor='blue')

# Secondary axis for temperature
ax1_temp = ax1.twinx()
ax1_temp.set_ylabel('Temperature Accuracy (°C)', color='red')
ax1_temp.tick_params(axis='y', labelcolor='red')
temp_min1 = 0
temp_max1 = np.max(mu_measurement_SST_monthly) - D47c.OGLS23.T47(
    D47=D47c.OGLS23.T47(T=np.mean(mu_measurement_SST_monthly))[0] + 0.05
)[0]
ax1_temp.set_ylim(temp_min1, temp_max1)

ax1.set_title('D47 Accuracy by Data Type and Month')

# ---------------------------------------------------------
# --- Precision Plot (Top Left: D47) ---
for month in months:
    ax2.scatter(precision_D47.index, precision_D47[f"{month} D47 Std"], s=20, color=color_dict[month])

ax2.set_ylabel('D47 Precision (‰ I-CDES)\nUncertainty on Estimate (1 SD)', color='blue')
ax2.tick_params(axis='y', labelcolor='blue')

ax2_temp = ax2.twinx()
ax2_temp.set_ylabel('Temperature Precision (°C)', color='red')
ax2_temp.tick_params(axis='y', labelcolor='red')
temp_min2 = 0
temp_max2 = np.max(mu_measurement_SST_monthly) - D47c.OGLS23.T47(
    D47=D47c.OGLS23.T47(T=np.mean(mu_measurement_SST_monthly))[0] + 0.006
)[0]
ax2_temp.set_ylim(temp_min2, temp_max2)

ax2.set_title('D47 Precision by Data Type and Month')

# ---------------------------------------------------------
# --- Accuracy Plot (Bottom Right: δ18Oc) ---
for month in months:
    ax3.scatter(accuracy_d18Oc.index, accuracy_d18Oc[f"{month} d18Oc Mean"], s=20, label=month, color=color_dict[month])

ax3.set_xticks(accuracy_d18Oc.index)
ax3.set_xticklabels(accuracy_d18Oc.index, rotation=45, ha="right")
ax3.set_xlabel('Data Type')
ax3.set_ylabel('δ18Oc Accuracy (‰ VPDB)\n(Abs. Difference from Measurement Mean)', color='blue')
ax3.tick_params(axis='y', labelcolor='blue')
ax3.set_title('δ18Oc Accuracy by Data Type and Month')

# Secondary axis for temperature, based on d18Oc-temperature conversion used above
ax3_temp = ax3.twinx()
ax3_temp.set_ylabel('Temperature Accuracy (°C)', color='red')
ax3_temp.tick_params(axis='y', labelcolor='red')
temp_min3 = 0
temp_max3 = np.max(mu_measurement_SST_monthly) - (20.6 - 4.34 * (((20.6 - np.max(mu_measurement_SST_monthly)) / 4.34  - 0.27) + 1.4 + 0.27))
ax3_temp.set_ylim(temp_min3, temp_max3)

# ---------------------------------------------------------
# --- Precision Plot (Top Right: δ18Oc) ---
for month in months:
    ax4.scatter(precision_d18Oc.index, precision_d18Oc[f"{month} d18Oc Std"], s=20, color=color_dict[month])

ax4.set_ylabel('δ18Oc Precision (‰ VPDB)\nUncertainty on Estimate (1 SD)', color='blue')
ax4.tick_params(axis='y', labelcolor='blue')
ax4.set_title('δ18Oc Precision by Data Type and Month')

# Secondary axis for temperature, based on d18Oc-temperature conversion used above
ax4_temp = ax4.twinx()
ax4_temp.set_ylabel('Temperature Precision (°C)', color='red')
ax4_temp.tick_params(axis='y', labelcolor='red')
temp_min4 = 0
temp_max4 = np.max(mu_measurement_SST_monthly) - (20.6 - 4.34 * (((20.6 - np.max(mu_measurement_SST_monthly)) / 4.34  - 0.27) + 0.7 + 0.27))
ax4_temp.set_ylim(temp_min4, temp_max4)

# ---------------------------------------------------------
# Shared legend above all plots
handles1, labels1 = ax1.get_legend_handles_labels()
fig.legend(handles1, labels1,
           loc="upper center",
           bbox_to_anchor=(0.5, 1.01),
           ncol=len(months),
           frameon=False)

# Hide top x-axis labels
ax2.tick_params(axis='x', labelbottom=False)
ax4.tick_params(axis='x', labelbottom=False)

plt.tight_layout(rect=[0, 0, 1, 0.95])  # leave space for legend
plt.show()

fig, (ax1, ax3) = plt.subplots(
    2, 1, figsize=(8, 10), sharex='col'
)
fig.subplots_adjust(hspace=0.1, wspace=0.25)  # reduce vertical & horizontal spacing

# Define a colormap across all months
cmap = plt.cm.coolwarm
colors = [cmap(i / (len(months)-1)) for i in range(len(months))]
color_dict = dict(zip(months, colors))

# Define offsets for x-axis to avoid overlapping error bars
x_offsets = np.linspace(-0.3, 0.3, len(months))

# Define x values for each data type
x_values = np.arange(len(all_uncertainty_test_table_df.index))

# --- D47 plot ---
for month in months:
    ax1.errorbar(
        x = x_values + x_offsets[months.index(month)],
        y = all_uncertainty_test_table_df[f"{month} D47 Mean"],
        yerr = all_uncertainty_test_table_df[f"{month} D47 Std"],
        capsize = 3,
        fmt='.',
        label=month,
        color=color_dict[month]
    )
# Add light green rectangle to highlight prior
ax1.add_patch(
    Rectangle(
        (-0.5, ax1.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax1.get_ylim()[1] - ax1.get_ylim()[0],  # height
        color='lightgreen',
        alpha=0.3,
    )
)
# Add light blue rectangle to highlight measurement
ax1.add_patch(
    Rectangle(
        (0.5, ax1.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax1.get_ylim()[1] - ax1.get_ylim()[0],  # height
        color='lightblue',
        alpha=0.3,
    )
)
# Add light red rectangle to highlight posteriors
ax1.add_patch(
    Rectangle(
        (1.5, ax1.get_ylim()[0]),  # (x,y)
        14,         # width
        ax1.get_ylim()[1] - ax1.get_ylim()[0],  # height
        color='red',
        alpha=0.1,
    )
)
ax1.set_xticks(x_values)
ax1.set_xticklabels(all_uncertainty_test_table_df.index, rotation=45, ha="right")
# ax1.set_xlabel('test case')
ax1.set_ylabel('D47 value (‰ I-CDES)', color='purple')
ax1.tick_params(axis='y', labelcolor='purple')

# Secondary axis for temperature
ax1_temp = ax1.twinx()
ax1_temp.set_ylabel('D47 Temperature (°C)', color='purple')
ax1_temp.tick_params(axis='y', labelcolor='purple')
ax1_temp.set_yticks(
    ticks = D47c.OGLS23.T47(T = np.linspace(0, 50, 25))[0],
    labels = np.linspace(0, 50, 25).astype(int)
)
ax1_temp.set_ylim(ax1.get_ylim())

# --- δ18Oc Plot ---

for month in months:
    ax3.errorbar(
        x = x_values + x_offsets[months.index(month)],
        y = all_uncertainty_test_table_df[f"{month} d18Oc Mean"],
        yerr = all_uncertainty_test_table_df[f"{month} d18Oc Std"],
        capsize = 3,
        fmt='.',
        label=month,
        color=color_dict[month]
    )
# Add light green rectangle to highlight prior
ax3.add_patch(
    Rectangle(
        (-0.5, ax3.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax3.get_ylim()[1] - ax3.get_ylim()[0],  # height
        color='lightgreen',
        alpha=0.3,
    )
)
# Add light blue rectangle to highlight measurement
ax3.add_patch(
    Rectangle(
        (0.5, ax3.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax3.get_ylim()[1] - ax3.get_ylim()[0],  # height
        color='lightblue',
        alpha=0.3,
    )
)
# Add light red rectangle to highlight posteriors
ax3.add_patch(
    Rectangle(
        (1.5, ax3.get_ylim()[0]),  # (x,y)
        14,         # width
        ax3.get_ylim()[1] - ax3.get_ylim()[0],  # height
        color='red',
        alpha=0.1,
    )
)
ax3.set_xticks(x_values)
ax3.set_xticklabels(all_uncertainty_test_table_df.index, rotation=45, ha="right")
ax3.set_ylabel('δ18Oc value (‰ VPDB)', color='darkblue')
ax3.tick_params(axis='y', labelcolor='darkblue')

# Secondary axis for temperature, based on d18Oc-temperature conversion used above
ax3_temp = ax3.twinx()
ax3_temp.set_ylabel('δ18Oc Temperature (°C; assuming δ18Ow of 0‰)', color='darkblue')
ax3_temp.tick_params(axis='y', labelcolor='darkblue')
ax3_temp.set_yticks(
    ticks = ((20.6 - np.linspace(0, 50, 25)) / 4.34  - 0.27) + 0 + 0.27,
    labels = np.linspace(0, 50, 25).astype(int)
)
ax3_temp.set_ylim(ax3.get_ylim())
ax3.set_title('δ18Oc value by test case and Month')

# ---------------------------------------------------------
# Shared legend above all plots
handles1, labels1 = ax1.get_legend_handles_labels()
fig.legend(handles1, labels1,
           loc="upper center",
           bbox_to_anchor=(0.5, 1.01),
           ncol=len(months) / 2,
           frameon=False)

plt.tight_layout(rect=[0, 0, 1, 0.95])  # leave space for legend
plt.show()

# Prepare the data for the table
data = {
    "Data Type": [
        "Prior estimates",
        "In situ measurements",
        "Individual Measurements",
        "Individual Measurements (SD D47 * 10)",
        "Individual Measurements (SD d18Oc * 10)",
        "Individual Measurements (both SDs * 10)",
        "Individual Measurements (SD D47 * 0.1)",
        "Individual Measurements (SD d18Oc * 0.1)",
        "Individual Measurements (both SDs * 0.1)",
        "Aggregated Measurements",
        "Aggregated Measurements (SD D47 * 10)",
        "Aggregated Measurements (SD d18Oc * 10)",
        "Aggregated Measurements (both SDs * 10)",
        "Aggregated Measurements (SD D47 * 0.1)",
        "Aggregated Measurements (SD d18Oc * 0.1)",
        "Aggregated Measurements (both SDs * 0.1)"
    ]
}

# Add monthly means and standard deviations to the data dictionary
months = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"]

# Process and rename the means and standard deviations for each data source
SST_means_prior = D47c.OGLS23.T47(D47 = mu_prior_SST_D47_monthly_original, sD47 = cov_prior_SST_D47_monthly_original, return_covar = True)[0]
SST_stds_prior = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_prior_SST_D47_monthly_original, sD47 = cov_prior_SST_D47_monthly_original, return_covar = True)[1]))

SST_means_individual = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC, sD47 = cov_post_SST_D47_monthlySC, return_covar = True)[0]
SST_stds_individual = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC, sD47 = cov_post_SST_D47_monthlySC, return_covar = True)[1]))
SST_means_individual_hu_d47 = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_HU_D47, sD47 = cov_post_SST_D47_monthlySC_HU_D47, return_covar = True)[0]
SST_stds_individual_hu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_HU_D47, sD47 = cov_post_SST_D47_monthlySC_HU_D47, return_covar = True)[1]))
SST_means_individual_hu_d18o = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_HU_d18O, sD47 = cov_post_SST_D47_monthlySC_HU_d18O, return_covar = True)[0]
SST_stds_individual_hu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_HU_d18O, sD47 = cov_post_SST_D47_monthlySC_HU_d18O, return_covar = True)[1]))
SST_means_individual_hu = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_HU, sD47 = cov_post_SST_D47_monthlySC_HU, return_covar = True)[0]
SST_stds_individual_hu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_HU, sD47 = cov_post_SST_D47_monthlySC_HU, return_covar = True)[1]))
SST_means_individual_lu_d47 = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_LU_D47, sD47 = cov_post_SST_D47_monthlySC_LU_D47, return_covar = True)[0]
SST_stds_individual_lu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_LU_D47, sD47 = cov_post_SST_D47_monthlySC_LU_D47, return_covar = True)[1]))
SST_means_individual_lu_d18o = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_LU_d18O, sD47 = cov_post_SST_D47_monthlySC_LU_d18O, return_covar = True)[0]
SST_stds_individual_lu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_LU_d18O, sD47 = cov_post_SST_D47_monthlySC_LU_d18O, return_covar = True)[1]))
SST_means_individual_lu = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_LU, sD47 = cov_post_SST_D47_monthlySC_LU, return_covar = True)[0]
SST_stds_individual_lu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthlySC_LU, sD47 = cov_post_SST_D47_monthlySC_LU, return_covar = True)[1]))

SST_means_aggregated = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated, sD47 = cov_post_SST_D47_monthly_aggregated, return_covar = True)[0]
SST_stds_aggregated = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated, sD47 = cov_post_SST_D47_monthly_aggregated, return_covar = True)[1]))
SST_means_aggregated_hu_d47 = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_HU_D47, sD47 = cov_post_SST_D47_monthly_aggregated_HU_D47, return_covar = True)[0]
SST_stds_aggregated_hu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_HU_D47, sD47 = cov_post_SST_D47_monthly_aggregated_HU_D47, return_covar = True)[1]))
SST_means_aggregated_hu_d18o = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_HU_d18O, sD47 = cov_post_SST_D47_monthly_aggregated_HU_d18O, return_covar = True)[0]
SST_stds_aggregated_hu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_HU_d18O, sD47 = cov_post_SST_D47_monthly_aggregated_HU_d18O, return_covar = True)[1]))
SST_means_aggregated_hu = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_HU, sD47 = cov_post_SST_D47_monthly_aggregated_HU, return_covar = True)[0]
SST_stds_aggregated_hu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_HU, sD47 = cov_post_SST_D47_monthly_aggregated_HU, return_covar = True)[1]))
SST_means_aggregated_lu_d47 = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_LU_D47, sD47 = cov_post_SST_D47_monthly_aggregated_LU_D47, return_covar = True)[0]
SST_stds_aggregated_lu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_LU_D47, sD47 = cov_post_SST_D47_monthly_aggregated_LU_D47, return_covar = True)[1]))
SST_means_aggregated_lu_d18o = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_LU_d18O, sD47 = cov_post_SST_D47_monthly_aggregated_LU_d18O, return_covar = True)[0]
SST_stds_aggregated_lu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_LU_d18O, sD47 = cov_post_SST_D47_monthly_aggregated_LU_d18O, return_covar = True)[1]))
SST_means_aggregated_lu = D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_LU, sD47 = cov_post_SST_D47_monthly_aggregated_LU, return_covar = True)[0]
SST_stds_aggregated_lu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SST_D47_monthly_aggregated_LU, sD47 = cov_post_SST_D47_monthly_aggregated_LU, return_covar = True)[1]))

SAT_means_prior = D47c.OGLS23.T47(D47 = mu_prior_SAT_D47_monthly_original, sD47 = cov_prior_SAT_D47_monthly_original, return_covar = True)[0]
SAT_stds_prior = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_prior_SAT_D47_monthly_original, sD47 = cov_prior_SAT_D47_monthly_original, return_covar = True)[1]))

SAT_means_individual = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC, sD47 = cov_post_SAT_D47_monthlySC, return_covar = True)[0]
SAT_stds_individual = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC, sD47 = cov_post_SAT_D47_monthlySC, return_covar = True)[1]))
SAT_means_individual_hu_d47 = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_HU_D47, sD47 = cov_post_SAT_D47_monthlySC_HU_D47, return_covar = True)[0]
SAT_stds_individual_hu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_HU_D47, sD47 = cov_post_SAT_D47_monthlySC_HU_D47, return_covar = True)[1]))
SAT_means_individual_hu_d18o = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_HU_d18O, sD47 = cov_post_SAT_D47_monthlySC_HU_d18O, return_covar = True)[0]
SAT_stds_individual_hu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_HU_d18O, sD47 = cov_post_SAT_D47_monthlySC_HU_d18O, return_covar = True)[1]))
SAT_means_individual_hu = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_HU, sD47 = cov_post_SAT_D47_monthlySC_HU, return_covar = True)[0]
SAT_stds_individual_hu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_HU, sD47 = cov_post_SAT_D47_monthlySC_HU, return_covar = True)[1]))
SAT_means_individual_lu_d47 = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_LU_D47, sD47 = cov_post_SAT_D47_monthlySC_LU_D47, return_covar = True)[0]
SAT_stds_individual_lu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_LU_D47, sD47 = cov_post_SAT_D47_monthlySC_LU_D47, return_covar = True)[1]))
SAT_means_individual_lu_d18o = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_LU_d18O, sD47 = cov_post_SAT_D47_monthlySC_LU_d18O, return_covar = True)[0]
SAT_stds_individual_lu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_LU_d18O, sD47 = cov_post_SAT_D47_monthlySC_LU_d18O, return_covar = True)[1]))
SAT_means_individual_lu = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_LU, sD47 = cov_post_SAT_D47_monthlySC_LU, return_covar = True)[0]
SAT_stds_individual_lu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthlySC_LU, sD47 = cov_post_SAT_D47_monthlySC_LU, return_covar = True)[1]))

SAT_means_aggregated = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated, sD47 = cov_post_SAT_D47_monthly_aggregated, return_covar = True)[0]
SAT_stds_aggregated = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated, sD47 = cov_post_SAT_D47_monthly_aggregated, return_covar = True)[1]))
SAT_means_aggregated_hu_d47 = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_HU_D47, sD47 = cov_post_SAT_D47_monthly_aggregated_HU_D47, return_covar = True)[0]
SAT_stds_aggregated_hu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_HU_D47, sD47 = cov_post_SAT_D47_monthly_aggregated_HU_D47, return_covar = True)[1]))
SAT_means_aggregated_hu_d18o = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_HU_d18O, sD47 = cov_post_SAT_D47_monthly_aggregated_HU_d18O, return_covar = True)[0]
SAT_stds_aggregated_hu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_HU_d18O, sD47 = cov_post_SAT_D47_monthly_aggregated_HU_d18O, return_covar = True)[1]))
SAT_means_aggregated_hu = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_HU, sD47 = cov_post_SAT_D47_monthly_aggregated_HU, return_covar = True)[0]
SAT_stds_aggregated_hu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_HU, sD47 = cov_post_SAT_D47_monthly_aggregated_HU, return_covar = True)[1]))
SAT_means_aggregated_lu_d47 = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_LU_D47, sD47 = cov_post_SAT_D47_monthly_aggregated_LU_D47, return_covar = True)[0]
SAT_stds_aggregated_lu_d47 = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_LU_D47, sD47 = cov_post_SAT_D47_monthly_aggregated_LU_D47, return_covar = True)[1]))
SAT_means_aggregated_lu_d18o = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_LU_d18O, sD47 = cov_post_SAT_D47_monthly_aggregated_LU_d18O, return_covar = True)[0]
SAT_stds_aggregated_lu_d18o = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_LU_d18O, sD47 = cov_post_SAT_D47_monthly_aggregated_LU_d18O, return_covar = True)[1]))
SAT_means_aggregated_lu = D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_LU, sD47 = cov_post_SAT_D47_monthly_aggregated_LU, return_covar = True)[0]
SAT_stds_aggregated_lu = np.sqrt(np.diag(D47c.OGLS23.T47(D47 = mu_post_SAT_D47_monthly_aggregated_LU, sD47 = cov_post_SAT_D47_monthly_aggregated_LU, return_covar = True)[1]))

# Combine all means and standard deviations into the data structure
all_SST_means = [
    SST_means_prior,
    mu_measurement_SST_monthly,
    SST_means_individual,
    SST_means_individual_hu_d47,
    SST_means_individual_hu_d18o,
    SST_means_individual_hu,
    SST_means_individual_lu_d47,
    SST_means_individual_lu_d18o,
    SST_means_individual_lu,
    SST_means_aggregated,
    SST_means_aggregated_hu_d47,
    SST_means_aggregated_hu_d18o,
    SST_means_aggregated_hu,
    SST_means_aggregated_lu_d47,
    SST_means_aggregated_lu_d18o,
    SST_means_aggregated_lu
]
all_SST_stds = [
    SST_stds_prior,
    std_measurement_SST_monthly,
    SST_stds_individual,
    SST_stds_individual_hu_d47,
    SST_stds_individual_hu_d18o,
    SST_stds_individual_hu,
    SST_stds_individual_lu_d47,
    SST_stds_individual_lu_d18o,
    SST_stds_individual_lu,
    SST_stds_aggregated,
    SST_stds_aggregated_hu_d47,
    SST_stds_aggregated_hu_d18o,
    SST_stds_aggregated_hu,
    SST_stds_aggregated_lu_d47,
    SST_stds_aggregated_lu_d18o,
    SST_stds_aggregated_lu
]

all_SAT_means = [
    SAT_means_prior,
    mu_measurement_SAT_monthly,
    SAT_means_individual,
    SAT_means_individual_hu_d47,
    SAT_means_individual_hu_d18o,
    SAT_means_individual_hu,
    SAT_means_individual_lu_d47,
    SAT_means_individual_lu_d18o,
    SAT_means_individual_lu,
    SAT_means_aggregated,
    SAT_means_aggregated_hu_d47,
    SAT_means_aggregated_hu_d18o,
    SAT_means_aggregated_hu,
    SAT_means_aggregated_lu_d47,
    SAT_means_aggregated_lu_d18o,
    SAT_means_aggregated_lu
]
all_SAT_stds = [
    SAT_stds_prior,
    std_measurement_SAT_monthly,
    SAT_stds_individual,
    SAT_stds_individual_hu_d47,
    SAT_stds_individual_hu_d18o,
    SAT_stds_individual_hu,
    SAT_stds_individual_lu_d47,
    SAT_stds_individual_lu_d18o,
    SAT_stds_individual_lu,
    SAT_stds_aggregated,
    SAT_stds_aggregated_hu_d47,
    SAT_stds_aggregated_hu_d18o,
    SAT_stds_aggregated_hu,
    SAT_stds_aggregated_lu_d47,
    SAT_stds_aggregated_lu_d18o,
    SAT_stds_aggregated_lu
]

# Create a dictionary to store all the data
all_temperature_data = {"Data Type": data["Data Type"]}

# Add SST means and stds
for i, month in enumerate(months):
    all_temperature_data[f"{month} SST Mean"] = [means[i] for means in all_SST_means]
    all_temperature_data[f"{month} SST Std"] = [stds[i] for stds in all_SST_stds]

# Add SAT means and stds
for i, month in enumerate(months):
    all_temperature_data[f"{month} SAT Mean"] = [means[i] for means in all_SAT_means]
    all_temperature_data[f"{month} SAT Std"] = [stds[i] for stds in all_SAT_stds]

# Create the Pandas DataFrame
all_temperature_uncertainty_test_table_df = pd.DataFrame(all_temperature_data)

# Set the 'Data Type' column as the index
all_temperature_uncertainty_test_table_df = all_temperature_uncertainty_test_table_df.set_index("Data Type")

# Export the table to a CSV file
all_temperature_uncertainty_test_table_df.to_csv("Sensitivity_test_D47_d18Oc_uncertainties/all_temperature_uncertainty_test_table.csv")

print("Combined data exported to Sensitivity_test_D47_d18Oc_uncertainties/all_temperature_uncertainty_test_table.csv")

Combined data exported to Sensitivity_test_D47_d18Oc_uncertainties/all_temperature_uncertainty_test_table.csv

fig, (ax1, ax3) = plt.subplots(
    2, 1, figsize=(10, 8), sharex='col'
)
fig.subplots_adjust(hspace=0.1, wspace=0.25)  # reduce vertical & horizontal spacing

# Define a colormap across all months
cmap = plt.cm.coolwarm
colors = [cmap(i / (len(months)-1)) for i in range(len(months))]
color_dict = dict(zip(months, colors))

# Define offsets for x-axis to avoid overlapping error bars
x_offsets = np.linspace(-0.3, 0.3, len(months))

# Define x values for each data type
x_values = np.arange(len(all_temperature_uncertainty_test_table_df.index))

# --- SST plot ---
for month in months:
    ax1.errorbar(
        x = x_values + x_offsets[months.index(month)],
        y = all_temperature_uncertainty_test_table_df[f"{month} SST Mean"],
        yerr = all_temperature_uncertainty_test_table_df[f"{month} SST Std"],
        capsize = 3,
        fmt='.',
        label=month,
        color=color_dict[month]
    )
# Add light green rectangle to highlight prior
ax1.add_patch(
    Rectangle(
        (-0.5, ax1.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax1.get_ylim()[1] - ax1.get_ylim()[0],  # height
        color='lightgreen',
        alpha=0.3,
    )
)
# Add light blue rectangle to highlight measurement
ax1.add_patch(
    Rectangle(
        (0.5, ax1.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax1.get_ylim()[1] - ax1.get_ylim()[0],  # height
        color='lightblue',
        alpha=0.3,
    )
)
# Add light red rectangle to highlight posteriors
ax1.add_patch(
    Rectangle(
        (1.5, ax1.get_ylim()[0]),  # (x,y)
        14,         # width
        ax1.get_ylim()[1] - ax1.get_ylim()[0],  # height
        color='red',
        alpha=0.1,
    )
)
ax1.set_xticks(x_values)
ax1.set_xticklabels(all_temperature_uncertainty_test_table_df.index, rotation=45, ha="right")
# ax1.set_xlabel('test case')
ax1.set_ylabel('SST (degrees C)', color='purple')
ax1.tick_params(axis='y', labelcolor='purple')

# # Secondary axis for temperature
# ax1_temp = ax1.twinx()
# ax1_temp.set_ylabel('SST Temperature (°C)', color='purple')
# ax1_temp.tick_params(axis='y', labelcolor='purple')
# ax1_temp.set_yticks(
#     ticks = D47c.OGLS23.T47(T = np.linspace(0, 50, 25))[0],
#     labels = np.linspace(0, 50, 25).astype(int)
# )
# ax1_temp.set_ylim(ax1.get_ylim())

# --- SAT Plot ---

for month in months:
    ax3.errorbar(
        x = x_values + x_offsets[months.index(month)],
        y = all_temperature_uncertainty_test_table_df[f"{month} SAT Mean"],
        yerr = all_temperature_uncertainty_test_table_df[f"{month} SAT Std"],
        capsize = 3,
        fmt='.',
        label=month,
        color=color_dict[month]
    )
# Add light green rectangle to highlight prior
ax3.add_patch(
    Rectangle(
        (-0.5, ax3.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax3.get_ylim()[1] - ax3.get_ylim()[0],  # height
        color='lightgreen',
        alpha=0.3,
    )
)
# Add light blue rectangle to highlight measurement
ax3.add_patch(
    Rectangle(
        (0.5, ax3.get_ylim()[0]),  # (x,y)
        1,                          # width
        ax3.get_ylim()[1] - ax3.get_ylim()[0],  # height
        color='lightblue',
        alpha=0.3,
    )
)
# Add light red rectangle to highlight posteriors
ax3.add_patch(
    Rectangle(
        (1.5, ax3.get_ylim()[0]),  # (x,y)
        14,         # width
        ax3.get_ylim()[1] - ax3.get_ylim()[0],  # height
        color='red',
        alpha=0.1,
    )
)
ax3.set_xticks(x_values)
ax3.set_xticklabels(all_temperature_uncertainty_test_table_df.index, rotation=45, ha="right")
ax3.set_ylabel('SAT (degrees C)', color='darkblue')
ax3.tick_params(axis='y', labelcolor='darkblue')

# # Secondary axis for temperature, based on d18Oc-temperature conversion used above
# ax3_temp = ax3.twinx()
# ax3_temp.set_ylabel('SAT Temperature (°C; assuming δ18Ow of 0‰)', color='darkblue')
# ax3_temp.tick_params(axis='y', labelcolor='darkblue')
# ax3_temp.set_yticks(
#     ticks = ((20.6 - np.linspace(0, 50, 25)) / 4.34  - 0.27) + 0 + 0.27,
#     labels = np.linspace(0, 50, 25).astype(int)
# )
# ax3_temp.set_ylim(ax3.get_ylim())
# ax3.set_title('SAT value by test case and Month')

# ---------------------------------------------------------
# Shared legend above all plots
handles1, labels1 = ax1.get_legend_handles_labels()
fig.legend(handles1, labels1,
           loc="upper center",
           bbox_to_anchor=(0.5, 0.95),
           ncol=len(months) / 2,
           frameon=False)

plt.suptitle('Sensitivity Test Results: Temperature Estimates under Different Uncertainty Scenarios', fontsize=16)
plt.tight_layout(rect=[0, 0, 1, 0.95])  # leave space for legend
plt.show()

month	lat	lon	ar	ag	dc	fb	ja	jl	jn	mr	my	nv	ot	sp
0	7.5	-81.5	27.870666	28.807864	28.234173	27.020926	27.569698	28.706740	28.716516	27.074181	28.717969	28.279754	28.346880	28.698233
1	7.5	-80.5	26.808416	27.472491	28.242612	26.442010	27.180057	27.630609	27.446476	26.412426	27.232879	28.372525	27.958568	27.736655
2	7.5	-79.5	26.814397	28.957019	28.453653	26.170235	27.295458	28.806538	28.734703	26.018813	28.156229	28.510441	28.605194	28.915533
3	7.5	-78.5	26.891758	29.054418	28.537700	26.116582	27.303514	28.938615	28.816935	26.014780	28.164300	28.650586	28.788851	29.053953
4	7.5	-77.5	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

month	lat	lon	ar	ag	dc	fb	ja	jl	jn	mr	my	nv	ot	sp
0	7.5	-81.5	27.583176	26.552208	26.558420	26.835735	26.682741	26.458174	26.592540	27.186361	27.313580	26.218864	26.229807	26.476027
1	7.5	-80.5	27.275017	26.536266	26.511211	26.583742	26.550386	26.459099	26.570900	26.928097	27.066269	26.204203	26.266203	26.487984
2	7.5	-79.5	27.001470	26.600628	26.552113	26.399340	26.497887	26.529715	26.607323	26.664957	26.917267	26.256363	26.311296	26.543280
3	7.5	-78.5	26.625885	26.183826	26.066435	26.162770	26.128641	26.111752	26.153196	26.438007	26.403248	25.779915	25.811575	26.081343
4	7.5	-77.5	26.058582	25.183080	24.992147	25.759280	25.274055	25.143060	25.183006	26.192318	25.495410	24.729294	24.765930	25.051905

month	lat	lon	ag	ar	dc	fb	ja	jl	jn	mr	my	nv	ot	sp
0	7.5	-84.5	30.189136	31.977873	31.473394	30.929856	30.345405	30.069491	30.195029	31.414025	32.039624	30.546265	29.788526	29.800602
1	7.5	-83.5	29.721171	32.084429	30.293614	30.814989	29.829491	30.040615	29.755975	31.457839	31.915529	30.029132	29.261298	29.054229
2	7.5	-82.5	29.425948	32.328173	29.279388	30.813826	29.614315	29.724405	29.525366	31.731921	31.874593	29.038743	28.927378	28.785658
3	7.5	-81.5	29.718203	32.912211	29.224964	31.114077	29.523134	29.884337	29.375634	32.313844	31.924800	28.856813	28.677410	28.918779
4	7.5	-80.5	28.278848	33.240089	28.165424	32.267726	30.310458	29.069918	28.696457	32.986556	31.064224	28.199434	27.682365	27.385693

month	lat	lon	ar	ag	dc	fb	ja	jl	jn	mr	my	nv	ot	sp
0	7.5	-81.5	1.689385	12.423080	2.590541	0.387124	0.582265	12.162777	11.670250	0.545877	6.474045	7.746123	11.768444	12.815062
1	7.5	-80.5	1.779216	12.493553	2.881293	0.449284	0.714600	12.262433	11.679930	0.586808	6.634595	7.909942	11.458197	12.675345
2	7.5	-79.5	2.001780	12.659093	3.562033	0.458198	0.814399	12.203677	11.351872	0.630577	7.039908	9.019142	12.075278	12.758909
3	7.5	-78.5	2.500152	13.219075	4.115735	0.685854	1.062848	12.568253	11.503000	0.875989	7.622621	9.605698	12.277294	13.266212
4	7.5	-77.5	3.386591	13.334969	4.033405	0.920459	1.207844	12.501793	11.494451	1.238471	8.514819	9.458278	12.520760	13.403852

month	lat	lon	ag	ar	dc	fb	ja	jl	jn	mr	my	nv	ot	sp
0	7.0	-81.5	31.136181	33.602102	29.170102	32.022884	30.418702	31.581640	32.324151	33.077173	33.040741	29.530418	30.622286	30.665430
1	7.0	-80.0	30.547831	33.757785	29.370818	33.184081	31.357592	30.910315	31.892236	33.637193	33.068963	29.336099	29.891578	29.889138
2	7.0	-79.5	30.542582	33.867599	29.344715	33.139511	31.427747	31.004266	31.869194	33.656158	33.013782	29.361235	29.827726	30.019896
3	7.0	-79.0	30.390912	33.637158	29.144642	32.730496	31.008538	31.002376	31.710107	33.398851	32.775925	29.262633	29.721688	29.765914
4	7.0	-78.5	30.493174	33.578397	29.022538	32.151029	30.534165	31.075004	31.585485	33.202158	32.854144	29.120639	29.612904	29.680376

INTRO¶

Notebook for applying Data Assimilation on modern data (Based on Caldarescu et al., 2021 data from Gulf of Panama)¶

Assemble data in the proxy domain using offline (block update) assimilation instead of point-by-point¶

Assemble data in SST (D47), SAT (D47), SSS (d18Oc) and precipitation domain (SSS data as measurements, not modelled)¶

Load packages¶

PRIOR - MONTHLY¶

Load monthly SST model data¶

Load monthly SAT model data¶

Load monthly SSS model outcomes (HadGEM3-GC31-LL 1995-2014)¶

Load monthly precipitation data¶

Combine SST, SAT, SSS and precipitation data by lat and lon¶

Calculate the monthly prior for model SST, SAT, SSS and precipitation values¶

Plot the monthly priors for all model values¶

Convert SST and SAT model data to D47 domain using the regression by Daëron and Vermeesch (2023) and propagate uncertainty in the calibration¶

Estimate seawater oxygen isotope value from salinity based on modern Gulf of Panama d18Ow-salinity relationship by Graniero et al. (2017; rainy season)¶

Calculate carbonate oxygen isotope value from SST and seawater oxygen isotope data using Grossman and Ku (1986) with the VPDB-VSMOW scale correction by Gonfiantini et al. (1995) and Dettman et al. (1999)¶

Calculate the monthly prior for model SST- and SAT-derived D47 values and SSS-derived seawater oxygen isotope values with propagated uncertainty¶

Plot the monthly prior for model SST- and SAT-derived D47 values, model SSS-derived carbonate d18O values and precipitation with propagated uncertainty¶

Calculate the monthly covariance matrix for D47 values of SST and SAT, d18Oc and precipitation¶

Plot normalized monthly covariance matrix between D47 values of SST and SAT, d18Oc and precipitation¶

Create combined monthly state vector in D47 and d18Oc domain¶

PRIOR - SEASONAL¶

Seasonal model data (convert the IPCC_Atlas data to seasonal means)¶

Calculate the seasonal prior for model SST, SAT, SSS and precipitation with propagated uncertainty¶

Plot the seasonal prior for model SST, SAT, SSS and measured precipitation¶

Calculate the seasonal prior for model SST and SAT-derived D47 values with propagated uncertainty¶

Plot the seasonal prior for model SST- and SAT-derived D47 values, d18Oc values and precipitation with propagated uncertainty¶

Calculate the seasonal covariance matrix for D47 values derived from SST and SAT values, d18Oc and precipitation¶

Plot normalized seasonal covariance matrix between D47 values of SST and SAT, d18Oc and precipitation¶

Create combined seasonal state vector¶

OBSERVATIONS¶

Load clumped data for updating¶

Monthly and seasonal data based on age model¶

Prepare measurement and observation matrices¶

Observations parsed as individual values¶

Measurement matrix for individual D47 values¶

Monthly observation matrix for individual D47 data¶

Observations on seasonal scale¶

Observation matrix for seasonal D47 and d18Oc data from individual D47 and d18Oc values¶

Measurement matrix for seasonally aggregated D47 values¶

Observation matrix for seasonally aggregated D47 data¶

Observations on monthly scale¶

Measurement matrix for monthly aggregated D47 values¶

Observation matrix for monthly aggregated D47 data¶

DEFINE UPDATING FUNCTIONS¶

Create updating function (Kalman filter)¶

Create function to track the statistics of the likelihood (combining just the reconstruction data)¶

TEST UPDATING FUNCTIONS' SENSITIVITY TO INPUT UNCERTAINTY¶

Load measurement data on SST, SAT, SSS and precipitation¶

SST measurement data¶

Convert SST measurement data to D47 for comparison in D47 domain¶

SSS measurement data¶

Load SSS ESA satellite data¶

Extract monthly and seasonal measurement data¶

Estimate seawater oxygen isotope value from SSS based on modern Gulf of Panama d18Ow-salinity relationship by Graniero et al. (2017; rainy season)¶

Calculate d18Oc values from d18Ow and SST values using Grossman and Ku (1986) with the VPDB-VSMOW scale correction by Gonfiantini et al. (1995) and Dettman et al. (1999)¶

SAT measurement data¶

Precipitation measurement data¶

Sensitivity testing for role of uncertainty and aggregation of data¶

Aggregate data while testing different combinations of enhanced uncertainty¶

Print D47 posteriors and uncertainties in a table¶

Print d18Oc posteriors and uncertainties in a table¶

Plot results of uncertainty test with increased uncertainty on D47 (SST) assimilation¶

Plot results of uncertainty test with reduced uncertainty on D47 (SST) assimilation¶

Plot results of uncertainty test with increased uncertainty on d18Oc assimilation¶

Plot results of uncertainty test with reduced uncertainty on d18Oc assimilation¶

Aggregate statistics on posterior outcomes on SST-D47 and d18Oc for all cases¶

Plot accuracy and precision in function of uncertainty¶

Extract data on accuracy and precision¶

Combine plots of accuracy and precision¶

Combined plot of measurements, priors and posteriors with precision uncertainties¶

Aggregate statistics on posterior outcomes on SST and SAT for all cases¶

Combined plot of measurements, priors and posteriors with precision uncertainties for temperature¶

Potential avenues for further testing/exploration:¶